The way to fix this is have all the point calculation on the server and have the client send raw input (e.g. hold left arrow key 1 second, enter key press, hold left mouse button 2 seconds, etc.). Even then, attackers can still write bots to bypass your flash client (but the bots will have to send raw input). I understand implementing this is complex, but I think this is the most secure solution.
Adding a private key to the flash file may be enough of an obstacle for a casual game. However, it provides no real security, because someone can easily decompile the SWF.