Try the following: download the offline installer from http://helpx.adobe.com/flash-player/kb/installation-problems-flash-player-windows.html#mai n-pars_header and save it to disk, then close all browser windows, right-click on the downloaded installer and select Run as Administrator.
If that still fails, please post the contents of the FlashInstall.log file from the C:\Windows\system32\Macromed\Flash folder.
