They can be carried by a Quetz, but you have to keep dunking them in water so they don't roast your bird.

Just waterboard them while traveling to a higher population taming ground, that has oodles of low level critters with babies to cook....I mean tame with!

Drop it in the shallows near your desired taming spot and quickly dismount and engage the flame kitty as it swims toward you. Knock its health down until it lets you ride it, then dive into the target rich environment you chose to set aflame.

I've tamed some nice Pyromanes in this manner with minimal issue! Avoid targeting birds, Cerats, Allos or anything else with high health, the ability to fly away or health regen. They're almost guaranteed to mess up the taming efficiency.