Not much. They probably have Damascus (twist) barrels, making them dangerous to fire even if otherwise tight and working. "Barker" was one of several names used to fool a customer into thinking he was buying a good quality gun (Parker) instead of a mediocre hunting gun.
Those guns are still quite common, and rarely bring more than $25 or so; quite a few are deactivated and used as decorators. For more info, see:
http://www.briley.com/articles/grampas_shotgun.html
Jim