Not really. As long as you ensure that your Win8 clients have the latest updates, you've ensured that they have the latest Flash Player. Given that you're resource constrained and the problem space around keeping Flash Player updated has been simplified considerably in this environment, perhaps it's an opportunity to re-evaluate the policies that require you to do this kind of tracking on Windows 8 and higher.
It’s more or less a enterprise security requirement now to know exactly what we got everywhere. To add another thing into the mix – we don’t use windows update, so our machines are kept current by another patch management solution. Therefore my question about how to check version in registry (patch management solution’s preferred method).
You can use the registry entry to find the version installed.
ActiveX: HKEY_LOCAL_MACHINE\SOFTWARE\Macromedia\FlashPlayerActiveX > Version
Plugin: HKEY_LOCAL_MACHINE\SOFTWARE\Macromedia\FlashPlayerPlugin > Version
This is much better than the entry in add/remove programs.