Flamehound is a enemy from Final Fantasy IV: The After Years. It is encountered throughout the game in various tales with varying levels of power.
In Edge's Tale, a scripted encounter with two Flamehounds occurs when Izayoi rejoins the party. While they hit hard and Izayoi and Tsukinowa have low HP, the player may wish to spend time having Tsukinowa and Edge Steal and Mug the Flamehounds to get a set of Fire Arrows for Izayoi, the only way they can be obtained in Edge's Tail.
Against all the incarnations of the Flamehound, it is dangerous to leave them alone, as under such circumstances they can use their powerful special attack, Blaze. When with other enemies, it is of no threat.