You have to have firmware 2.7 or higher. Then you have to turn on flash in Settings ---> System Settings ---> Enable Flash Player.
Put the .swf files on the root level of your memory stick (just makes it easier), launch the web browser and for the web address put in file:/game.swf where "game.swf" is the name of the file on your memory stick.
If you find a game you like, I suggest bookmarking it, that way you don't have to type in "file:/" etc etc etc every time you'd like to load a flash game.
Good luck.
Bookmarks