I second the first reply that flash is inferior to HTML and CSS, partly due to SEO drawbacks.
However, if you want to get a screenshot, a way that could work is to get a full screenshot of your webage. You could then put it into an HTML file, and add the needed title tags into that file, and then put it in a subdomain such as "p.yourdomain.com". Then just stick in a 301 redirect on that subdomain to your real site, link to the new subdomain on Facebook, and that should work!