Flame Gun

Flame Gun is a firearm. It inflicts fire-based damage onto targets and is thus more effective against enemies with a weakness to fire-based attacks.

Source
Flame Gun can be purchased from arms vendors in Altissia, Cartanica, Tenebrae, and Gralea for 5,000 gil. It can also be found as a collectable in the Pitioss Ruins. It can be sold back to shops for 2,500 gil.