The two heads occasionally disagree on trivial matters like who to eat first.

Twinflame Tyrant

Flying
If a source you control would deal damage to an opponent or a permanent an opponent controls, it deals double that damage instead.

"Job only paid enough for one head. I'm out."
—Peren, veteran mercenary

Foundations

If another effect (or effects) modifies how much damage a source you control would deal—by preventing some of it, for example—the player being dealt damage or the controller of the permanent being dealt damage chooses the order in which any such effects (including Twinflame Tyrant's) apply. If all of the damage is prevented, Twinflame Tyrant's effect no longer applies.

If damage dealt by a source you control is being divided or assigned among multiple permanents and/or players, that damage is divided or assigned before doubling. For example, if you attack with a 5/5 creature with trample and it's blocked by a 2/2 creature, you can assign 2 damage to the blocker and 3 damage to the defending player. Those amounts are then doubled to 4 and 6, respectively.

The damage is dealt by the same source as the original source of damage. The doubled damage isn't dealt by Twinflame Tyrant unless it was the original source of damage.