I'm thinking the functionality in Area51, where hovering over the icon of a site shows the reputation on that site in the tooltip.
The only official flair format is the image format offered via your profile page. You could take a look at http://stackapps.com and search for flair there.
Of the flair options on StackApps, I'd recommend http://stackflair.com personally though. (: You can get an html version which provides tooltips for the different elements.
Since HTML does not allow you to assign alt or title texts to specific parts of an image, and since non-image based flair is not available, this is not possible through Stack Exchange, nor is it likely to be offered, based on the following quote:
What about the old, non image based flair?
The earlier methods of sharing flair are deprecated and will go away eventually. Please use the simpler image flair from this point onward!