Flash Player 9 does not allow keyboard input when displaying content in full-screen mode.
Flash Player 10 changes this, allowing for a limited number of keys to be usable in full-screen mode. These include Tab, the Spacebar, and the (up, down, left, right) arrow keys.
That makes sense. You can't really get over that when it is inherent in Flash. I guess the only thing you can do is show a notice to let people know when going into full-screen mode.