Hmm...is it wise to add a Fire-type to a team that already has a Rock-type (soon to be Steel-type) and an Electric-type? That's a whole lotta Ground weakness. Seriously, Kadabra can wipe out most of Celadon Gym by itself because there are only two pokémon in that whole place that aren't Grass/Poison. Not two species, although that's also true; two individual pokémon.
Anyway, assuming you do decide a Fire-type's worth the risk, I would be remiss not to point out the glaring flaw in choosing a Flareon at this point in the game. Since the Eevee available in Celadon Mansion is over level 16, and you can't breed yet, your Flareon won't have a Fire attack until level 36, at which point it learns Fire Spin. Tactically useful, perhaps, but not impressive damagewise. After that you'll have to wait until level 52 for Flamethrower. The only solution to this dilemma would be to get the TM 35 from Rocket Game Corner; do you have the cash and/or luck to do that?
Vulpix, on the other hand, learns Flamethrower naturally at a very reachable level 29...think it over.