Hydrogen peroxide is a good choice for fuel for this sort of application. However I wonder if the hydrogen peroxide would decompose spontaneously if it came into contact with an epoxy-kevlar composite tank?

Whether his capsule survives or not depends on his peak dynamic pressure and Mach number. If he stays under Mach 3 then his composite capsule would heat up a bit but might avoid delamination. However the force of dynamic pressure on the capsule's surface would be enormous. Dynamic pressure goes as velocity squared. Imagine the force of wind blowing against your hand if you stick it out your car's window while cruising on the freeway at 60 mph. Now imagine you're going 600 mph and that force is 100 times greater. A problem the Germans had with their old V-2 rockets (and the Iraqi's with their Scuds) was the dynamic pressure would cause the missles to breakup during descent from apogee. There are too many uncertainties with his design. If this guy is riding his rocket on its maiden flight then he's probably committing suicide.

Gary