I hate to be the bearer of bad news, but you won't be able to have Flareon (or Jolteon/Vaporeron, for that matter) for a loooong time. You don't get a fire stone until you beat all of the Johto region and get to Cerulean in the Kanto region.
You can catch a Growlithe on routes 36 & 37, which are very close to where you said you're at. It'd be a great choice to catch if you didn't have to complete 3/4 of the game before you can get a fire stone to evolve him. I went through a whole game with little Growlithe on my team though, so it's very possible. :P
You can also catch Magmar in the Brass Tower in Ecruteak... they're not a bad choice either.