Joe,
It's actually a bit of Javascript that you'd have to include on the page to log the user out. Just to make sure, you want to actually log the user out of LinkedIn altogether, not just destroy the cookie that says they are logged into your site, correct?
I'll have to look into the best way to do that, but I think the code should be easy.. however, you may have to add it to quite a few places since there are many logout buttons scattered throughout JomSocial. There isn't one central place that you can modify the code to log them out, just so you know.
Thanks,
Alex