It is a prize from the mauville game corner labeled TM 35
You can get TM 25 (Flamethrower) at the Mauville Game Corner for 4000 coins.
You can trade a Pokemon that is holding the TM from diamond to soulsilver or pearl or platinum or you can migrate a Pokemon holding the TM from ruby, sapphire or emerald or firered or leafgreen.
To get Flamethrower (TM35) you must win 4,000 coins in the MAUVILLE GAME CORNER which you can find in Mauville. This place is located between route 117 and route 118.
TM11(Sunny Day) TM35(Flamethrower) TM38(Fire Blast) TM50(Overheat)
Oh, that's easy.Earn it.........
You only can learn flamethrower if you have a fire-type pokemon. Look for TM35.
Pokemon Ruby has Pokemon that Pokemon Sapphire does not and Pokemon Sapphire has Pokemon that Pokemon Ruby does not.
First of all...Flamethrower isn't even a Pokemon! Flamethrower is a Pokemon move! Your Pokemon has to EARN it, by getting to higher levels. Mainly Fire-type Pokemon earn Flamethrower. Hope this helps!-JinJiAlso you can buy the HM (at least in FR,LG (the other GEN 3 games))inside the casino
Palkia can learn flamethrower with a TM otherwise NO
Vulpix learns Flamethrower at level 35.
It learns Flamethrower at level 34.
Houndoom learns Flamethrower at lvl 48.