Strange slipping issue..

Ok,.1966 Valiant, Slant 6, 904 trans, 7 1/4 Sure grip. Had the car for only 2 weeks. Something strange is happening. When I drive the car normally, it shifts fine and well, is fine. When at a stop light and on heavy acceleration something feels like it's slipping and sounds like banging. When this happens and I let up and continue with normal acceleration,.it's fine. I'm wondering if it's the clutches in the rear? Trans is shifting fine with no slip at all. This only happens when stopped on heavy acceleration. If I'm at 35/40 or more and if I hit it,.it's fine. Not sure what this is. Motor mounts are fine and trans mount is fine. It has me stumped so far. Any ideas of what this could be? If it's the clutches in the rear,.how is this checked?