Here are the Fire-type moves it can learn via TM/HM:
* TM25 Thunderbolt: (Learned from a TM)
* TM38 Fire Blast: (Learned from a TM)
* TM49 Flamethrower: (Learned from a TM)
* TM50 Overheat: (Learned from a TM)
However, Ponyta can learn Ember via level-up, which is a Fire-type move. It also learns Quick Attack at level 15, which is a Normal-type move that can be a good complement to Fire-type attacks.
If you want to make Ponyta a Fire-type powerhouse, you'll have to teach it these moves through TMs or breeding.