The REST API is what you'd use to check if the user is a member of a certain group. The check likely wouldn't be too difficult to add to our authentication flow as we have special points where checks can be performed to prevent a login for various reasons.
We could gladly point you in the right direction and help with what you're looking to do. However, it's not something we'd implement right now in JLinked or JFBConnect as it's not a highly requested feature. We're also in the midst of some deep development with JFBConnect right now so, if we do decide to develop this, it'd be a lower priority item.
Again, if you have a developer, we can gladly point you in the right direction and help get the code going, but it's not something we'd develop.
I hope that helps answer your question, but should you need anything else, just let me know.
Thanks,
Alex