Looks like the image itself isn't animated (at least not any more). My guess is when the avatar is resized, the animation is stripped out of it. You could get around this by providing a URL to the image instead of uploading it (where it will be resized and de-animated).
You would have to upload them to a free server like photobucket, and then use the tag it provides in your signature box.. it will provide you three tags, the one you want looks like this but without the spaces
Got it flying in sig block, but not as an avatar. The profile update page doesn't seem to like updating it. When I paste the URL into the second option it shows the flying pie. Once I click update it changes it to static pie and shows that I have uploaded a custom pic.
Very strange. Might have to go ponder this over some pie...