We’ve had good success with the following for all Windows operating systems (one property to rule them all!)
ActiveX version
unique values of (versions of files (values “PlayerPath” of keys “HKEY_LOCAL_MACHINE\SOFTWARE\Macromedia\FlashPlayerActiveX” of (registries;native registries) as string))
Plugin version
unique values of (versions of files (values “PlayerPath” of keys “HKEY_LOCAL_MACHINE\SOFTWARE\Macromedia\FlashPlayerPlugin” of (registries;native registries) as string))
This will return a single value even if you theoretically have both 32- and 64-bit versions installed, as long as they are the same version.