It really depends on what you're talking about.
We do actually use fly to describe things that are up in the air but not literally flying, most notably, for flags.
As to the specific examples, there are many options. Including ones you note, there's flap, flutter, float, blow, billow, dance, ripple... and many more. It's all about what sort of emotion or feeling you want to give.
For example, pieces of fabric such as a curtain or sheet might be described to billow:
The curtains billowed in the breeze.
Or, in a stiffer breeze, to flutter:
Flags fluttered in the breeze.
If you want to be fancy, you could even say something like:
The clothes danced on the drying line.
This gives a very fun and energetic feel, the opposite of billow.
Hair, on the other hand, would probably float in a soft breeze or fly in a stiff wind.
When the breeze blew, her hair floated in front her her eyes, hiding them from my vision.
Her hair flew into her face as the wind blew around her.
Whichever word you use is part of the artistry of the English language. As you see above, words relating to both air and water movement are possible, and it's largely a matter of personal preference. If you start trying things out, be sure you are able to visualize the movement you're trying to describe.