If you're talking about a list of high scores of EVERYONE who has played a particular Flash game on a website, then you'll need something independent of the Flash game itself to keep track of it, b/c it'd be impossible for the Flash game to remember by itself.
If this is going to be on a website, then you'll need to know some PHP to do this.
Google search on Flash High Score Pages
If everybody is going to play this game on the same computer (which I doubt), then you could use Flash's Shared Object, which is basically a Flash cookie.
Google -> Flash shared object
You'll have to do some research! Good Luck!