A fusion/fission rocket engine using a pinch seems pretty blue-sky at this point, to be honest. Their paper[0] only briefly mentions the main problem with cylindrical geometries: "With a successful Phase II award the team will test at these varying power levels z-pinch processes to drive out the progression of plasma instabilities in a z-pinch process." Pinches are not very good at being stable, and they are what people tried before going to toroidal geometry (tokamaks et al). Of course, for pulsed power you don't need your pinch to be stable for very long, but at our current state of the art it's breathtakingly inefficient.
Fusion/fission hybrids have been mooted for power production, but there are several issues. First, why make your neutrons via fusion when that's essentially the most difficult way to do it? Second, once you put uranium into your reactor, you've got the same nuclear waste problem that you've got with fission, mucking up your arguably-much-cleaner fusion process. So there are significant downsides to a hybrid system.
0: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/2014001...