He cant. I tried to teach him fireblast but no. He got dragon breath in 50's but mine got to lv 100 without flamethrower.
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rapidash learns flamethrower if you get the TM flamethrower and teach it
fire punch
It takes a long time. You can either teach it a TM move flamethrower, breed a charmander, charmeleon or charizard with another Pokemon from the same group as it which knows flamethrower, or level up charmander to lv 32.
Only its former evolution, Growlthe, can learn it before it. When you evolve Arcanine, it cant learn ANY of growlthes moves, but can learn extreme speed at level 33. Or you could just teach Arcanine flamethrower by using the TM flamethrower, otherwise, you will have to level up a growlithe until it learns flamethrower then evolve it into an arcanine.
TM35 (Flamethrower) can only be found at the Mauville game corner. You need 4,500 tokens to get it. It'll cost you about 110000gp, but well worth it. Flamethrower-95 power, 100 accuracy. Recommendation? Teach it to Absol. He's a Dark-type, but for some reason, he can learn Flamethrower.