"Downloading" is one thing.
"Installing" is another entirely.
Download the applicable file(s) (or all of them) for your OS and browser:
Save these files - DO NOT run them yet.
Reboot your system.
BEFORE opening anything, go to your Downloads folder and run the UNINSTALLER first to remove all instances of Flash Player.
Then run the installer(s) to replace the Flash Player with the new version.