The flapping looks really unnatural because the wings only move up and down, as opposed to moving left and right as well.
It might look nice to have the bird's body move down a bit when it flaps upwards, and upwards when it flaps downwards. You already do this a bit but the downward motion stops at a certain point for some reason.
You might also want to move the head down to make it more aerodynamic-looking.
Also, please note that many birds only flap to take off, and often glide to maintain flight. It all depends on wingspan though, since their wings might not be large enough to hold their weight while gliding.
Another problem is the frames or frame rate, the downward flapping motion is a very slow, fluid motion, when in reality it is a fast, powerful and somewhat jerky motion. Think of it like punching someone in slow motion, it isn't going to do much because it's going so slowly.
The wings seem like a triangle, attached to the body when they flap up, which, unless this is a feature unique to this bird, is anatomically incorrect.
http://www.google.com/images?oe=UTF-8&gfns=1&q=bird+wings&um=1&ie=UTF-8&source=univ&ei=sHb1S-naBJC4swPOgLGIBQ&sa=X&oi=image_result_group&ct=title&resnum=1&ved=0CCgQsAQwAABird wings have a somewhat small attachment to the body, and their long flight feathers usually become even longer at the ends.
You have a rather defined chest right there, but it barely moves, giving the bird a lifeless look. I have a pet bird, and I can easily say that they have a very clear motion in their chest when they breath.
When flying in mid-air birds often tuck their feet into their body, so that they are covered by their feathers. This makes them much more aerodynamic. Smaller birds do this, and I'm pretty sure large birds of prey do it as well.
The bird in that video was taking off, and probably planning to grab onto the railing the whole time, so he wouldn't have tucked in his feet anyway.
The head looks like it's attached to the body, take advantage of a neck being there to make it look more lifelike, make it move around, whatever you want.
The tail looks odd, for birds flying mid-air the tail is usually small and flat. It only really fans out when landing, because it slows the bird down.
The bird's body is pointed slightly upwards. this makes it looks like the bird is trying to go upwards rather than stay at the same altitude. This may be on purpose, but it looks kind of odd.
One last thing is the bird's colors, usually female birds are less colorful, while males are colorful and pretty so that they can win the ladies!
But, this bird looks like it's somewhere in-between.
Purple is also an odd color for most birds, as they usually are colorful to warn off predators or to camouflage. Purple serves neither purpose, as red or yellow would be warning colors, while blue, green, and brown would be camouflage colors.
As a side note, the bird being brown would mean it would spend most of it's time on the ground rather than on the air, being that it would want to blend in with the ground. You might also want to consider what kind of feet this bird has. Having three toes in front and one in the back means it want lots of traction when walking around, while having two in the back and front means it want a good grip on branches.
The purple also ruins the camouflage, as purple is a pretty rare color in the animal world.
Also, this looks less like a hawk, and more like a pigeon to me. Usually hawks have big, beefy, yellow legs and talons for swooping and grabbing stuff.
This bird looks like it has little pink stick legs, the direct opposite...
Otherwise, it looks good. Nice job on all of those frames by the way!
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Oh, my. I seem to have written an essay analyzing your art.
Well, I hope it helps!
