Download the FULL Offline installer: Flash Player 22.214.171.124 Plug-in (Mac OS X) by right clicking and selecting "Download Linked File As".
Save it and Quit Safari (Cmd+Q)
Double click the DMG
and "mount it" on your desktop.
A window will open showing the Installer - DO NOT RUN IT!
Right click (Ctrl+click or two(2) finger tap on a trackpad) and "Show Package Contents".
In Contents/Resources, double click the Adobe Flash Player.pkg
Follow the steps to run the COCOA installer.
Then eject the DMG by right clicking