I'm quite sure Blizzard didn't intend for this to happen however, if you're on Fire in the Skies and an enemy also takes the quest and mounts up, if you're close enough to him, if you auto attack by right clicking the enemy fire hawk your fire hawk will hit the other fire hawk for 5-6K every hit (not too sure if damage is based on your weapon on just the hawk it's self).
This is especially cruel because I believe you have to retake the quest and there is no way of getting back to your corpse without getting resurrection sickness.