Ian- They do flap, but they don't like it! I like that shadow too Peter. No bird in flight is an easy photographic target so you did well to get this. Harsh lighting is a challenge as well, especially with a black bird.
With the combo of the 7D and that great 400mm lens, and a slight crop I am surprised that the image is not sharper. I'm not getting a sense of detail on my monitor and wonder if a round of sharpening may improve the image. Not sure because not all images respond to this. The other thing I might try is a different crop with more space at the top.
I'm also thinking it's just not quite as crisp as it could be. The eye seems rather sharp but the head and wings overall seem soft on my monitor.
I'm wondering, too, about the angle of the bird in the frame. Was it rising or flying straight ahead? It might possibly need a bit of rotation if it was more on an even keel.
Hmmm .... I'm not sure. Head looks sharp but not the wings ... I don't understand that one myself. 1/2000 should have been fast enough to stop motion blur on the wings, shouldn't it? Maybe it is all just slightly OOF except for the head at f/6.3? Is that a possibility? I'm heading back to my RAW file to see what I can figure out.