Point your browser to:
http://www.macromedia.com/support/documentation/en/flashplayer/help/settings_manager07.html
You should see a screen like this:
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Now click on the site you want to want to clean up and click on Delete Website, or you can just click on Delete all sites.
You are all set to get the new version of the flash video or flash game you were looking for.
Thanks to the team at BlindValet.com for the tip.
Enjoy,