I've not had any luck with Facebook or Google+ games on the RT. Not sure why, I'm running the latest version of Flash, tried Desktop and Metro modes and even used the whitelist app to make sure they were good.
Some of the flash games will work, even on Facebook. Bejeweled blitz by pop cap games, and Zima blitz works fine. Their was some mmo on Facebook that I got to work by editing the whitelist.(you must view the source code of the webpage and see where the flash game is coming from. Whitelisting Facebook won't make the games work, you have to whitelist the original site.)
A lot of the games with good graphics also use Java, so those ones won't work.