train a charizard, he'll learn it eventually
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no it doesent so you should better evolve vulpix at level 26 it actually learns flamethrower at level 29
You only can learn flamethrower if you have a fire-type pokemon. Look for TM35.
Houndoom learns Flamethrower at lvl 48.
It learns Flamethrower at level 34.
TM35 (Flamethrower) is located in the Abundant Shrine.