If you use Chrome as your browser, then you don't need to bother with installing Flash Player; Chrome comes with Flash Player embedded.
The latest Chrome version will always contain the latest Flash Player.
I'm having the same problem with Google chrome but on Windows 7 32-bit system...Any ideas?? I have reinstalled the latest versions, and any updates, and I still cannot play any Flash videos...
As I wrote, Chrome already comes with Flash Player preinstalled; you cannot uninstall or install it.
Maybe it needs to be enabled? It's really a Chrome issue.
Could you please type the following in Google Chrome's address bar: chrome://plugins
Click Details and see if there are entries for Flash?