If the client (i.e. flash) is keeping track of/generating the score, there is no secure way for you to send the score to the server. Whatever the swf file can do, an attacker can also imitate.
The only secure way is to send each user move or action to the server. The server is responsible for the state of the game and maintaining the score; the client just generates the moves.
With such an approach, an attacker cannot manipulate the score. He can still bypass your SWF file, but to get a high score he still has to make the right moves. The attacker can make a bot to make the moves intelligently; to avoid that you can only use security by obscurity.