I’ve had several different types of flight in my dreams, but I’ve never had air-swimming. The most common is probably super-jumping: I can run down the street, my feet only touching down every block or so. In mid-jump I can decide “I don’t think I’ll land yet; I’ll wait until I get past that landmark”, but I can’t generally stay aloft indefinitely (if I do, it transitions into some other flight type). I think this comes from riding my bike, which is something I do often: It’s similar to a running motion, but much smoother, and you can choose to only “step” once every great distance.
Also common, is the ability to levitate. Typically, I start this by bending both my legs at the knees (without falling, of course), and holding my ankles in my hands behind my back (I have no idea of the origin of this pose). Once free of the ground in this manner, I can rise and descend as far as I’d like, but I can’t generally move horizontally. Occasionally, I’ll have the reverse of this, where I take off the same way, but can’t rise further, but I can propel myself forward.
Rarely, and most fun, I find myself with complete control of my movement. I can swoop, climb, dive, soar, loop-de-loop, etc., completely independently of any motions I might make. Of the dreams I remember, I can almost always do at least one of these types of flight, which is indeed a lot of fun.