Flareon can be evolved from Eevee through the use of a Fire Stone. Eevee can be found in the Celadon Mansion.
Fire Stones may be bought in Celadon City. A free Fire Stone can be found in Mt. Ember.
Okay, what are you doing? Vaporeon has awesome bulk, Jolteon's a speed demon, and what's Flareon? Uh... nothing that's really any good. Its movepool is garbage, its stats are all in the wrong places, and it's overshadowed by the other two Eeveelutions and pretty much all other Fire-types in-game. However, if you insist on using it, Flareon has one or two things going for it. For one, it's the bulkiest Fire-type (specially, that is) in-game, and it's also one of the best anti-Psychic Pokémon in this generation thanks to the lack of Dark-types. While Flareon might not be very good, it can be put to good use.
Gym #3 - Lt. Surge (Vermillion City, Electric-type): Flareon is pretty good here, actually; it's better than Vaporeon and Jolteon, and might be able to do some damage with Dig. However, the only way you'd have Flareon before this battle is if you bypassed Lt. Surge in the first place and went straight for Rock Tunnel, in which case you'd have a pretty overleveled team with which to crush his Pokémon underfoot anyway.
Rival (Pokémon Tower): Flareon can pretty effectively handle everything that your rival carries except for Gyarados or Wartortle. Even Charmeleon and Growlithe are beaten with Dig, while they can't do much back to you. STAB Flamethrower or even just some Normal-type move such as Secret Power can lay on the hurt to the rest of his team.
Giovanni (Rocket Hideout, Ground-type): Even if Flareon carries Dig, Rhyhorn and Onix will give Flareon some issues thanks to their high Defense stats. Kangaskhan is also bulky enough to take whatever is thrown at it and will be hitting VERY hard with Mega Punch. Leave Flareon out of this.
Gym #4 - Erika (Celadon City, Grass-type): If you got the Flamethrower TM and taught it to Flareon, then wreck this Gym. If not, Flareon still makes for a good Grass-type move absorber, but it probably won't have the necessary tools to do sufficient damage.
Gym #5 - Koga (Fuchsia City, Poison-type): Flareon is capable of hitting very hard with STAB Flamethrower here (particularly to the Koffings and Weezings, which have low Special Defense), but for the most part, everything hits on the physical side, which is Flareon's weaker defensive stat. Don't even try against Muk, because it's extremely bulky and hits very hard.
Fighting Dojo (Saffron City, Fighting-type): Only let Flareon fight Hitmonchan. Other than that, don't let it near the very powerful Fighting-types, since, with its low Defense stat, it'll probably get wrecked.
Rival (Silph Co.): Flareon might be able to handle Pidgeot with its STAB moves, and whatever Grass-type he has will get wrecked. Keep it away from any Water-type. Flareon can effectively wall whichever Fire-type he has, whether its Charizard and its dangerous Flamethrowers or the weak NFE Growlithe, thanks to the ever-useful Flash Fire. Alakazam only has Future Sight, so feel free to let Flareon destroy this thing.
Giovanni (Silph Co., Ground-type): Again, keep Flareon away. Everything's the same except he has a Nidoqueen, which is too powerful and bulky for Flareon to take on. Plus, some of his Pokémon got major move upgrades, making them much more fit to kill Flareon.
Gym #6 - Sabrina (Saffron City, Psychic-type): Flareon is actually very fit to handle Sabrina. Flareon's awesome Special Defense allows it to take STAB Psychics and retaliate with strong physical moves, especially if you got the Shadow Ball TM and gave it to Flareon. Also, that Venomoth doesn't stand a chance.
Gym #7 - Blaine (Cinnabar Island, Fire-type): Flareon's Flash Fire allows it to act as a great Fire Blast/Flamethrower soaker-upper, since not many other Pokémon can handle a STAB Fire Blast from an Arcanine. However, Take Down from Arcanine will hurt like a son-of-a-gun, and Rapidash's annoying Stomp flinchhax combined with the annoying Bounce are worrisome.
Gym #8 - Giovanni (Viridian City, Ground-type): Do you want Flareon taking a STAB Earthquake to the face? I didn't think so.
Rival (Route 22, pre-Elite Four): Same things again, although now he has a Rhyhorn. Don't let Flareon fight that. Rock Blast hurts.
Elite Four Lorelei (Indigo Plateau, Ice-type): Flareon should sit this one out until she sends out Jynx. Unfortunately, Lovely Kiss + Attract makes Flareon miserable. However, if Lovely Kiss misses, then Flareon can rip apart Jynx with Flamethrower or Shadow Ball.
Elite Four Bruno (Indigo Plateau, Fighting-type): Another match for Flareon to sit out. Both Onix have Earthquake, and the Fighting-types have too strong STAB moves that will hit Flareon's low Defense. Not a great matchup for poor Flareon.
Elite Four Agatha (Indigo Plateau, Poison-type): If Flareon has Shadow Ball, then go all-out on her Ghosts. If not, it's probably a good idea to not let Flareon fight them. You might be able to take out Arbok with Dig, but Intimidate slows you down. Golbat's slightly fast and bulky, but it's more annoying than it is powerful, so Flareon shouldn't have too much trouble with it. If you want a clean sweep in this battle, go for an X Speed or two while she has her first Pokémon out. Shadow Ball from Flareon can reliably take out both of her Gengar as well as her Haunter, but you have to outspeed them first.
Elite Four Lance (Indigo Plateau, Dragon-type): Nothing Lance has should be handled by Flareon. Nothing.
Champion Rival (Indigo Plateau): Same as last time, except Arcanine's a little bit more dangerous than Growlithe used to be.
Post-Game: The fight with Mewtwo is where Flareon's anti-Psychic utility really proves useful. Flareon's high Special Defense allows it to take at least one non-critical Psychic from Mewtwo without healing, and Shadow Ball can do almost half in retaliation, with a worst case scenario Shadow Ball (0 EVs and 0 IVs and an Attack-hindering nature vs. a Bold Mewtwo with perfect IVs; a minimum damage roll, with both Pokémon at level 70) still doing more than a third to Mewtwo, while also having a decent chance to lower Special Defense, making the job easier for another team member to finish if need be.
Again, Flareon starts with Eevee's monstrosity of a moveset. Then (assuming it's evolved already), it learns Quick Attack at level 23, which is better on Flareon than any other Eeveelution. At level 30, it gets Bite, which is a decent move, but isn't the best. Then it gets its first STAB move at level 36... Fire Spin. Ha, no. At level 42 it gets Smog, which shouldn't even be considered. It gets even more laughable at level 47, where it gets a move many Pokémon start out with: Leer. Again, no. At level 52 it FINALLY learns a good level-up move, which is Flamethrower. However, you probably already gave it that move anyway.
Now, TMs and HMs are where you're going to patch up Flareon's terrible movepool. Roar might sound nice, but remember that foes rarely set up and you risk letting Flareon take a hit doing that. Toxic might sound fun, but Flareon doesn't like to stall. Hidden Power is interesting given Flareon's mixed attacking stats, but can be really terrible depending on the type. Sunny Day is fun, but it's not really too useful. Hyper Beam is good if you're playing on Shift, but if not, go for Return, Strength or Double-Edge. Protect isn't too useful because, again, Flareon isn't a staller. Rain Dance shouldn't need explaining. Frustration is near-useless because leveling up and walking raises happiness and the most reliable way to lower happiness is to let your Pokémon faint, which you can't do in a nuzlocke. Iron Tail is good for beating Rock-types, but is unreliable and situational. Also, don't let Flareon fight Rock-types. Dig is nice if you're not fighting anything with Earthquake (which you shouldn't be doing with Flareon anyway). Shadow Ball is a cool move for beating Psychic-types, which is honestly one of the very few things Flareon does better than most Pokémon in this game. Double Team, Rest, Attract, and Substitute could be useful. Flamethrower should be put on its moveset as soon as its obtained; likewise for Fire Blast. Facade is probably not your best option since opponents rarely inflict status. Secret Power is good for a short time, but should be replaced with Return or Double-Edge. Overheat is a cool move but its additional effect limits it to emergencies.
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.
What Nature do I want? Honestly, deciding this is very difficult. You really don't want to lower ANY of its stats since it needs all of them. However, lowering defenses is better than offenses or speed. The best ones are neutral natures, but Lonely, Mild, Naughty, or Rash are also useful. Any Attack, Special Attack, or Speed-lowering nature is pretty bad.
At what point in the game should I be evolved? Immediately, unless you don't know how to buy and use a Fire Stone, in which case you probably shouldn't be nuzlocking in the first place.
How good is Flareon in a Nuzlocke? Not going to sugar-coat it: it's pretty bad. If you want a Fire-type, go out and catch a Growlithe or Vulpix. If you can't, that doesn't really matter since the Kanto remakes aren't very nice to Fire-types anyway. If you want an anti-Psychic Pokémon, you're best off with Snorlax. Really, anything Flareon does anyone else can do better. Only use Flareon if it's your only option, or if you want a challenge.