My guess is your VPN provider intentionally doesn't support Flash because it's an outdated technology that can be exploited relatively easy. The idea of a VPN is privacy after all. Have you looked through your settings to see if there is an option for allow flash? Or different tiers of protection that you may be able to adjust?
If the settings aren't built into the VPN, look over the providers website and see if it's mentioned, if not contact them. There may be an easy fix, or it give you an excuse to get a refund and switch services. I personally use HideIPVPN and have never had issues regarding flash, or any other content issues.
If you don't care to play the games, Joe's score sender should work regardless if you're connected to a VPN or not.
I'll tinker around with the settings and see what it says next time I'm on that particular computer. Thanks for the ideas to troubleshoot, @(you need an account to see links)