Joe,
I'm not sure I know what you mean, or at least haven't seen or heard of the issue if I do understand.
Are you saying when user's click the "Login With LinkedIn" button, the user can go to three different locations? That's definitely not correct. If the user is new (unregistered), they should always go the standard Login / Register page of JLinked. If clicking that button directs you to the Joomla or JomSocial login page, that's definitely wrong. If you're clicking another button or link though, let us know, so we understand more.
Obviously, if the user has already registered, they should simply be logged in and go wherever you have your JLinked redirections setup for.
If the redirections are incorrect as in the first paragraph, check if you have any User or System plugins enabled that are meant to redirect the user for any reasons (logins, edit profiles, etc). There's a lot of plugins that are meant to redirect users for certain reasons, but it's always possible that one of those can conflict with our registration/login process. Let us know if you have anything like that.
Thanks,
Alex