captured the downbeat of the wings in this shot, and his beak open slightly. I got 2 shots of the downbeating wings and in both his beak is open, so maybe they breathe inwards on the downbeat of their wings?

Also notice they quite often "hook" one hind claw over the other foot when flying, as if to stabilize both feet once they get flying straight ahead. It is very interesting to watch all this happening : )