There is already a shortcut, but I'm not sure how many people know about it. 
To flip the board all you need to do is to press x.
Do you know you can use the arrow keys to move through moves in a game (not sure if this works while playing live chess or not)
Hope this helps!
Holy....!!!
A 1000 thanks! So in case you guys didn't know: Just press "x" and it flips the board.
(Way better than my suggestion of ALT + something, which triggers the browser's menu, I think)
KiwiTai thanks for telling me
At first I thought you meant flipping over the chess board as a way to resign in spectacular fashion! 
HEy there.
I was just wondering, is it possible to include a handy shortcut, say ALT + F, to flip the board?
I do this quite often - when re-visiting old games or even during play. Mouse navigation to the menu then flip icon is sometimes a bit awkward. ALT + F would be AWESOME!