Here's the deal:
-Flair pretty much demands a Facebook app
-I'm working on learning the Facebook platform
Therefore, I've written a dinky little Facebook app to embed your Flair into a box on the side of your profile. If you're interested and on Facebook; beware that this is very much a work in progress, prone to change and has a whole bunch of rough edges.
However, I don't have an elegant way to say "this is MY Stackoverflow profile" from this dinky app. My current solution is best demonstrated this image. It is, frankly, idiotic; and there's nothing preventing impersonation.
Having no experience with OpenID, I'm wondering if there's some way (and some example of this way, please) to get a user to provide their Stackoverflow identify to a third party?
Behavior changed to that suggested by Noldorin's answer.
Request for a saner way to do this declined on UserVoice.