Please go to https://get.adobe.com/flashplayer and download the installer. Locate where it was saved to on your system and double-click to launch it. Proceed with intallation.
If you select 'Allow Adobe to install updates (recommended)' at install time Flash Player will automatically update, silently in the background, within 24 hours of an update being released.
The link you have provided is broken. I get a 413 error. I'm using safari.
Please try clearing the browser cache, or at minimum, removing all *.adobe.com cookies from your browser.