I'm glad (but at the same time sad) someone has had the exact same problem I had.
I've tried a few things (though none successful).
- creating a flash pro project from the fb project
- creating an AS3 project from the as3 mobile project (which runs on air). now this one I thought would work, and it does in Flash Player, however, when I try to run it with the generated html file, all I get is a string of errors.
Here is something that does work.
If you create an AIR project in Flash Pro (I've only tried this in CS5.5), when you publish the project, it will generate the swf and html files and the html file works and the swf runs great. Unfortunately you have to start that way (which sucks for programmers that want the benefits of Flash Builder). I haven't found anything to properly convert it yet.
I hope this is some insight, even a year later.