Question: at what level does arcanine learn flamethrower?
Answer: One it has reached the magic 50 (when it learns the Flamethrower technique), use a Fire Stone to evolve it. Remember: if you evolve your Growlithe before Level 50, it will never learn Flamethrower. Although it's not quite as powerful as Fire Blast (which you can learn from TM 38), it's 100% accurate and never misses.