What I usually do in these cases is I'll promote the user encountering the issue to an Administrator level account. After that, I'll login to this user's account, which is now an administrative account. Once logged in, I will fully uninstall Flash Player using Adobe - Web Players
the Flash Player Uninstaller at that link.
After that, I will close any currently open browsers and then log off this user. Then log back in as this same user and go back to adobe.com and install Flash Player in IE then in Firefox (or Safari or whatever alternative browser you use, if you do it in one of them, it will work in any alternative browser for the most part.) After that, I will log off and login to another administrative account and demote this user back to a limited account and then Flash will work for them.
Try these steps and see if they work for you or not.