Flash stores cookies in the ~/Library/Preferences/Macromedia/Flash Player/#SharedObjects directory. These can be reset by trashing the #SharedObjects folder, which is used to store cookies for Flash, no matter which browser you are using. If doing this en masse (e.g. via Apple Remote Desktop or a patch management solution), then you can do so with the following command, which removes that folder for all users on the system (unless you’re using network homes or have customized the home folder location):
rm -fr /Users/*/Library/Preferences/Macromedia/Flash Player/#SharedObjects
