No, unfortunately it is not possible to combine the two accounts (games or statistics). Your Facebook Chess account and your Chess.com account are two separate things.
Link Facebook app with my chess.com account
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I'm right there with ya wishing I could link the two or use features like conditional moves on the FB side.
That aside; consigliori, I know nothing about that 'thingy' or if this idea will work, but if indeed that thing is designed to let you flaunt stats on other websites via a pic url or some simple html, there are apps on FB for such inserts. My favorite is called Profile Box, which you can actually add as a box, tab, or main page section with whatever html content you like. Worth a shot?
Is it possible to link my chess.com account to my facebook? I added the app to my facebook page and it created a new account.