A question has come up at our table. Would an antimagic field or dead magic zone effect the flight of an air elemental? They never state what kind of flying it is. I know they effect supernatural and spell like abilities. A dragons flight would work while a bone devils wouldnt.
But what about that elemental?
AtD
I would put it in that most rarely-mentioned category, natural abilities.
Natural Abilities: This category includes abilities a creature has because of its physical nature. Natural abilities are those not otherwise designated as extraordinary, supernatural, or spell-like.
The physical nature of air elemental is "a batch of air," for which flight seems pretty natural to me.
AFAIK nothing ever stops your natural abilities from working short of polymorphing into something else, so the AMF or dead magic area shouldn't affect the elemental's flight.