Barbarian Kings should be able to attack air units. They would have to jump which will double the time in between attacks. This would come in handy when you are attacking someone and a dragon comes out of your opponents clan castle, the Barbarian would essentially neutralize the dragon.
Archers (like 20 of them) can already neutralize dragons. Plus, a level 40 barb king does 576 damage per second. Do you really want him to be able to attack air units?