Chrome has its own proprietary Flash Player plguin ("PepperFlash") which is modified, embedded and maintained solely by Google.
Download the following files by right clicking and selecting "Save target as"
Save ALL files to your Downloads folder - DO NOT RUN anything yet.
Reboot your system.
BEFORE opening anything else, go to your Downloads folder and run the UNINSTALLER to remove all instances of Flash Player.
Next, run the ActiveX Installer.
Lastly, run the Installer for other browsers.
Once everything is installed, see:Enabling Flash Player in Internet Explorer and: ActiveX Filtering in Internet Explorer to make 100% sure that Flash Player is enabled and NOT being blocked by ActiveX controls.
If those steps still fail due to admin privileges needed,
You can get the MSI installers from http://www.adobe.com/products/flashplayer/distribution3.html
Note that it first lists the 64-bit installers, then the 32-bit versions.