Growlithe is available in HeartGold only on Routes 36, 37 and 38 in Johto, as well as 7 and 8 in Kanto. On Route 48 it's a certain encounter by using the Repel trick at night with a level 25 Pokémon at the front of the party.
Fire Stones may be obtained: from School Kid Alan, on Route 36, by getting his PokéGear number and receiving a call on Wednesdays; at the Pokéathlon Dome for 2,500P on Tuesdays or (after the National Dex) Thursdays and Sundays; from Bill's grandfather, by showing him a Vulpix in SoulSilver or a Growlithe in HeartGold; at the Bug Catching contest (after the National Dex) by winning the first prize.
Praise the Pokéathlon! We finally don't have to wait for those freaking NPCs to call us and give us a Fire Stone! Power and Speed Course are easy enough that you can prepare to get your fluffy beast to its full power.
Fire-types are relatively rare. And Arcanine is arguably the best you can get, especially if you didn't choose Cyndaquil. It's also the earliest one you can get, not counting Cyndaquil, as Flareon requires reaching Ecruteak and getting a Fire Stone, whereas Growlithe is ready to go should you encounter it on one of the two routes leading to Morty's city. On top of that, it's the only Fire-type (again, sans Cyndaquil) you're guaranteed to encounter under standard Nuzlocke rules if you don't ban the Repel trick for your challenge. Once you get that puppy you'll have something soon to become a fast mixed attacker that doesn't neglect its defenses. And it even has a good movepool! The only problem is that if you want to go physical, you need to wait for some moves. Ah, the questionable joys of stone evolutions.
Gym #3 - Whitney (Goldenrod City, Normal-type): You won't get much use of your freshly caught Growlithe here (if you got lucky on Route 36 or your previous catches made the puppy a guaranteed encounter here as well for Repel + dupes method). The most you can hope to do here is taking out her Clefairy, something that you might also want to leave for someone else, to set up for Miltank or sponge hits better in case of a nasty roll on Metronome. The fact that Growlithe has 75% chance to be male doesn't help either.
Rival (Burned Tower): Growlithe will be very helpful against his Magnemite, and if you chose Totodile as your starter, Bayleef as well. If you didn't get to start with Bite, don't worry - one or two Flamethrowers will take it out anyway, Zubat will face a similar fate. Croconaw is a bad idea, obviously, while Quilava would simply take too long. Unless you have Flash Fire. Then it'll be long, but easy.
Gym #4 - Morty (Ecruteak City, Ghost-type): Growlithe should handle Gastly and the second Haunter - the level 23 one. Gengar with its STAB Shadow Ball and the level 21 Haunter with the Mean Look + Hypnosis + Dream Eater combo pose too much of a threat, as they will both outspeed. Arcanine, on the other hand, if you spent some time Pokéathloning (and sacrificing Crunch and Flare Blitz in the process)? Tears through Morty's team and is ready for the dessert.
Eusine (Cianwood City): Better to attempt to fight the Drowzee with Bite in your arsenal, as taking too long will give the tapir time to set up its Hypnosis+Dream Eater combo or make it even slower with Disable. Haunter is more frail, so you're good to go with either Bite or Flamethrower. Electrode is a no. You do not want something faster than you to use STAB Thunder or start a Rollout.
Gym #5 - Chuck (Cianwood City, Fighting-type): Trainer's best friend is out of this battle. Both of Chuck's Pokémon carry its weaknesses (Primeape - Rock Slide, Poliwrath - Surf). Plus, they have the means to increase their chances of landing a Focus Punch in the form of Double Team and Hypnosis. You want something good against them to take them out as soon as possible. Your patience will be rewarded in the very next gym battle.
Gym #6 - Jasmine (Olivine City, Steel-type): You're in for a sweep. Steelix might require two Flamethrowers if the numbers are not good for you, but that's all. You outspeed and should take its Rock Throw pretty nicely.
Petrel (Team Rocket HQ): If you handled Jasmine before coming to Mahogany, you're more than ready for this fight. The sheer level difference from preparing for the previous leaders will make it so even the SelfDestruct Koffing is not a problem in this battle.
Ariana (Team Rocket HQ, tag battle with Lance): Sheer level difference plus an illegal Dragonite as your ally. Not sure if Team Rocket is even trying.
Gym #7 - Pryce (Mahogany Town, Ice-type): Pryce's Pokémon don't have Water moves. However, Piloswine has Mud Bomb and the two seals have Thick Fat (in addition to one of them not even being an Ice-type). If you still have Growlithe, you won't get a quick victory here. Arcanine will eat them.
Petrel (Goldenrod Radio Tower): Bad idea, very bad idea. Petrel closed the level gap a bit and even Selfdestruct from a Koffing is a major threat, let alone Explosion from a Weezing. If you decided to evolve your puppy though, it should have no problems with OHKOing the Koffings with Flamethrower, and outspeeding them is a given. But even in that case, leave Weezing for something bulky.
Rival (Goldenrod Underground): Generally, the same thing as before, with the addition of Sneasel, weak to Fire. Bayleef evolved though, so it's a bit bulkier. Facing the Water starter would be a bad idea anyway, so evolution here changes very little. Quilava is still the same, so if you have Flash Fire, enjoy the good laugh.
Proton (Goldenrod Radio Tower): Your STAB will take out Golbat, your special STAB - Weezing. Which can't explode.
Ariana (Goldenrod Radio Tower): Even without a dragon companion, you will easily dominate Ariana. Arbok doesn't have easily exploitable weaknesses for you unless you gave your puppy TM28 for Dig, so it will take at least two hits. You still outdamage it though.
Archer (Goldenrod Radio Tower): Can you make an origami dog? If yes, then good - you have an accurate representation of Archer's ace. However, if you're still postponing the evolution, your best option here is Dig - physical Normal moves you can get won't cut it. Arcanine, however, also 2HKOs the hellhound with Return, and with good stats, even Strength. Archer's other mons? Houndour is just the same, but made from a smaller sheet of paper. Koffing's best move is STAB Sludge. Team Rocket, ladies and gentlemen.
Gym #8 - Clair (Blackthorn City, Dragon-type): The only mon you can hope to fight is Gyarados - it has no Water moves, its best trick being Bite and Dragon Rage. However, even Return from Arcanine will be about 3HKO, so it'll be better to just exploit Gyarados' unfortunate typing. Kingdra is a definite no, while Dragonairs are a risky no. She has two, identical at first glance, until one of them uses Aqua Tail.
Kimono Girls (Ecruteak Dance Theater): Much of this matchup depends on Arcanine's moves. Umbreon goes down to patience and Fire STAB either way, but Espeon will need Crunch, because it can hit fairly hard. If you have Flash Fire, Flareon will be a joke, and if you have Intimidate it won't be much more threatening either, since its Last Resort becomes less powerful. Jolteon is about even in strength, but careful about Thunder Wave paralysis. Vaporeon? Absolutely not.
Ho-Oh (Bell Tower): Your Arcanine (from this point onwards it's automatically assumed you used the Fire Stone, Ho-Oh is approximately the level you get Flare Blitz, so you have no reason to postpone it any longer) will deal similar damage to Ho-Oh as Ho-Oh will deal to it, something vaguely around quarter. You, however, have healing. Defeating the rainbow bird will be easy, while for catching it's more recommended to use a bulky Water-type, that can also sponge Extrasensories.
Rival (Victory Road): By this point you have no reason to not have Crunch, so in combination with your STAB you already take care of four of your rival's Pokémon - Sneasel, Magneton, Kadabra and Haunter. Most of your arsenal will also make the skirmish with Golbat not too long or memorable, and if you picked up Thunder Fang from the move relearner, even less. Facing Feraligatr is still a bad idea, Waterfall is not a joke. Typhlosion got Lava Plume with evolution, so... well, exactly the same as before.
Elite Four Will (Indigo Plateau, Psychic-type): Crunch, Flamethrower, avoid Slowbro.
Elite Four Koga (Indigo Plateau, Poison-type): Three of his Pokémon are weak to Fire. If you're running physical or mixed, start with a lighter attack on Muk before deploying Flare Blitz, in case its Gunk Shot connects. All your moves should be 2HKO on Crobat, in case you don't have a quick Electric-type to handle it instead.
Elite Four Bruno (Indigo Plateau, Fighting-type): You generally want to avoid everything that is not Hitmonlee or Hitmonchan. Those two you can 2HKO with Flamethrower or OHKO with Flare Blitz, with the additional bonus of resisting three out of four of Hitmonchan's elemental punches (the fourth one is Bullet Punch).
Elite Four Karen (Indigo Plateau, Dark-type): Vileplume is a no-brainer. Umbreon will take at least two hits, not stopping annoying you. Defenses-wise, Murkrow is generally, well, Murkrow. Gengar is risky. You shouldn't have problems OHKOing it if you run physical with Flare Blitz, but the real problem is whether you outspeed or not. If the latter, you could face a nasty case of Destiny Bond. Houndoom you want to leave for someone else, Karen knows how to use that Pokémon better than Team Rocket.
Champion Lance (Indigo Plateau, Flying-type): This is not a fight for Arcanine. All it can contribute to it with is using Thunder Fang on Charizard. Don't worry, we still have Kanto! ...If you decide to go there.
From this point onwards, you can fight the gyms in any order, though you will need to retrieve the Machine Parts from the Cerulean City gym before you have access to the earlier portion of Kanto. Feel free to anticipate or postpone any battles as needed.
Gym #9 - Brock (Pewter City, Rock-type): Remember why Charmander has it rough in early game in the prequels? Exactly.
Rival (Mt. Moon, optional): More of the same battles. Alakazam and Gengar are evolved now, but they're equally vulnerable to Crunch and they can't off Arcanine in one go. Really, the only threat is once again Feraligatr, if you started with Cyndaquil.
Gym #10 - Misty (Cerulean City, Water-type): The pool should be enough of a suggestion that Arcanine should not be out in battle at any point. You could 2HKO Golduck with Thunder Fang, Starmie with Crunch and even Lapras with Flare Blitz, but the need to heal every other turn is not worth it.
Gym #11 - Lt. Surge (Vermilion City, Electric-type): In general, you want to leave this battle for a Ground-type. You could go with Dig, but be prepared for being outsped. And one of Surge's Electrodes carris Selfdestruct. Magneton is easy though.
Gym #12 - Erika (Celadon City, Grass-type): I'll tell you a joke. Erika against an Arcanine.
Gym #13 - Janine (Fuchsia City, Poison-type): Like father, like daughter. Three Pokémon weak to Fire. Steer clear from Weezing's Explosion and take on Crobat if you have no better options. There should be some.
Gym #14 - Sabrina (Saffron City, Psychic-type): You can sweep her with Crunch or Flare Blitz under one condition - equip a Choice Scarf. As a safety measure against Alakazam's STAB Psychic.
Gym #15 - Blaine (Seafoam Islands, Fire-type): Dig makes quick work of them. And if you have Flash Fire, Blaine's elaborate strategy that he certainly didn't steal from Flannery goes down the drain. Wouldn't it be a pretty... bold move to fight fire with fire (except don't. They resist Fire. Rapidash has Flash Fire)?
Gym #16 - Blue (Viridian City): Exeggutor is weak to Fire. If you kept Dig, you can have a nice mirror match against Arcanine, but note the possibility of it Roaring you away. Your STAB will make Pidgeot not any problem. Gyarados, Rhydon and Machamp should be avoided.
Rival (Indigo Plateau, optional): Possibly more samey than before, even, as Golbat became Crobat but literally nothing else has changed. Avoid Feraligatr as usual and pay attention to what outspeeds you when your health is low, that's all.
Red (Mt. Silver): Arcanine should outspeed Red's lead, the closest vanilla games had to Manlychu from Vega. And about what to use... can you make an origami rat? Yeah. Venusaur shouldn't cause problems, but make sure to watch out for the poison possibility from Sludge Bomb combined with the permanent hail. Or, well, as it's the final battle and there's nothing to lose, nuke it with Overheat. Bringing Sunny Day might be a good idea. Especially to nerf Blizzard, carried by half of his team. Snorlax is very bulky. You want to leave it for someone else, as it will outdamage you. Lapras and Blastoise you generally want to avoid. Charizard? Go for Thunder Fang, just like with Lance. Congratulations on getting here.
At the lowest level you can get it (i.e. 13 on Route 36), Growlithe knows Bite, Roar, Ember and Leer. This is the best possible situation, as starting from level 14 Bite will be overwritten with Odor Sleuth on the wilds you can get and by the time you reach the Move Reminder, you won't need Bite anymore. At level 17 you get Helping Hand, unsurprisingly not worth it. Level 20 gives you Flame Wheel, your physical choice for STAB until you can replace it with Fire Fang eight levels later. Before that, you can get Reversal at level 25, not the best type of move in a challenge where you'd rather stay as far from the red HP bar as possible. At level 31 you get Take Down, a questionable choice due to the recoil, especially that by that point you should have access to Strength and Return. Level 34 finally gets us to the level range with good skills. Flamethrower needs no introduction. Agility obtained ad 39 won't be of any real use. The best was saved for the end. Crunch at level 42 and Flare Blitz at 48. Patience shall be rewarded.
Arcanine adds two things to the pool: Thunder Fang, which is Heart Scale-only, as well as Extremespeed, at level 39.
Passed by Goldenrod? Unless you have the TM for Flamethrower with you... what are you doing? It's a staple for any special-oriented or mixed Arcanine. Or, well, any Fire-type. If you like playing with the weather, Sunny Day will be an excellent choice for quickly setting up. And if you do, why not top it with SolarBeam for coverage? Dragon Pulse sounds good on paper, but at most as an option for quick unresisted special damage should something be resistant to Fire. Not much for actual Dragons, as they can and will carry moves to counter you. Going physical? Return is an obvious and easy choice. And the funny thing is, all five TMs mentioned up to this point are available in Goldenrod City (Game Corner, gift after defeating Rockets, Dept. Store, lottery in Dept. Store and gift in Dept. Store respectively). Everyone likes puppies. Dig could work for variety at least for some part of the game, as Arcanine doesn't learn Earthquake. Kanto will grant you access to Overheat, but it's extremely late game and cutting your Special Attack in half is not the best idea in the long run, as your only sources of White Herbs are Battle Frontier and those three you can snatch from Blaine. Still, it's a good short term option, especially if you run a fully physical Arcanine with only Overheat as a special move. For utility your giant puppy can use Strength, Rock Smash and Rock Climb, the first being a decent pre-Kanto alternative should you give Return to someone else. If you're still in the early game, before Strength is available and before Return is at full power, it might be a good choice to briefly backtrack for Headbutt to Ilex Forest.
Special (Sun): Flamethrower, Crunch, Sunny Day, Solarbeam
Minimum stats are calculated with 0 EVs, IVs of 0, and a hindering nature, if applicable.
Maximum stats are calculated with 252 EVs, IVs of 31, and a helpful nature, if applicable.
Growlithe Line Ratings
What Nature do I want? With Arcanine's versatility, you can work with any. However, it's better to not have anything that lowers any of the attacking stats, unless you want to go mostly physical or mostly special, with the other being a bit neglected.
Which Ability do I want? This line is far more useful defensively with Intimidate, rather than Flash Fire. However, even Flash Fire Arcanine will be reliable team members, and could work wonders with their STAB with the right amount of prediction.
At what point in the game should I be evolved? Do you want to go full physical? If yes, at level 48 if you want Flare Blitz. If no, then at level 42 if you want Crunch for versatility or as soon as possible if all you want to do is Flamethrower all the things.
How good is the Growlithe line in a Nuzlocke? It deserves its place among the best Fire-types in Johto, being a serious pretender to the throne. It gets the job done without being a glass cannon. Has a movepool wider than Typhlosion. However, it's its movepool that causes main problems - only the lowest-level Growlithe available will have Bite, essential for big part of its usefulness throughout the first region. Crunch and Flare Blitz come very late, so you'll face the dilemma about whether to wait and let your puppy be benched for a while due to its stats not being high enough to keep up with its fully evolved teammates or to go for the Fire Stone and miss out on some moves. If you can get around that issue, you have quite a mighty puppy there.
Weaknesses: Ground, Rock, Water
Resistances: Grass, Bug, Steel, Ice, Fire (Intimidate)