Hi, First make sure you are using the Administrator Account. Download and SAVE to your Desktop this Flash Player Installer for Firefox:
Close all browser windows, disable an app in the system tray that uses Flash, messenger services, Anti-Virus that runs in realtime.
RUN the Installer from your Desktop and then Reboot your computer.
Test here and if you see the animation and the version number, then Flash Player has been Installed correctly.
Hope this works for you.