i loooove using a flamethrower in all fallout games, i dont know why, but the idea of burning anyone who bothers me is so awesome, 
i've been playing for 3 hours and haven't found one, unlike in fallout 3 where you could get 1 right out of the vault, if someone could tell me a location where i could get one that's relatively close to where you start, i will supply you with 268 Internets.

...try The Toolchest. GET IT? GET IT? WHERE TO FIND A FLAMER? LIKE A GAY PERSON? YEEEEEEEEEEEEEEEEEEEEEEEEEE-HAAAAAAAAAAAAAAAAAAAAAW

There's one in the silver rush, in Freeside, the main quest line will take you there.  You can pay for it or easily steal one with a stealthboy.

Theres also one in Primm. You gotta fight a dude for it though. In Big Steve or whatever the name of the casino is, lol, cant miss it theres only two big buildings.

" ...try The Toolchest. GET IT? GET IT? WHERE TO FIND A FLAMER? LIKE A GAY PERSON? YEEEEEEEEEEEEEEEEEEEEEEEEEE-HAAAAAAAAAAAAAAAAAAAAAW "

I picked up the one in Primm, then promptly sold it away because for some messed up Roleplaying reason I decided to go for a lighter strength for more luck.

Do you mean the incinerator?  Somehow I was able to find one within the first 30 minutes of the game, it's almost too powerful to have so early in the game.  I don't know where exactly I found it, or if it was pure luck or what, but yea I think it was just kinda laying around someone's dead body in the middle of nowhere...maybe near Primm?