Gert,
There's no way built-in to JLinked that would automatically fetch the user's LinkedIn profile URL and use that. The problem is that not all of your authors may have logged in via JLinked and, even if they did, we'd have to cache and store their member profile somewhere so that we don't have to look it up each time (slowing down each page).
We've considered looking into this feature for future versions, and have taken not of your feedback, but unfortunately, I don't know when we'd get this feature in. Just so I know, are you using Joomla Content articles or K2 for your blogs?
Thanks,
Alex