Ive done rocket powered Frisbees on and off since the 1970's. I made mine similar to some I saw flown on "I've got a Secret" (or some TV gameshow like it) in the early 70's.
A C6 engine in the center for upward thrust. A mini-A3 engine mounted to the rim to spin the model up. Both ignited at the same time as a cluster. Sometimes with a D12 in the center. The rim had a large notch cut into it for the spin motor mount to be anchored into (with epoxy), a good bit of the mount on the inside of the rim so the inside of the rim took the brunt of the centrifugal force loads, otherwise the spin engine could have easily been flung off.
Around 1977 or 1978, I made one with a single engine in the center. It was mechanically spun up, the engine plugged into the top of a motor mount diameter tube that was attached to the spin motor assembly. There were some homemade electrical brush contacts that carrier the current to a flashbulb ignitor inside (I used a flashbulb because the brush system was not designed to be able to deliver a lot of current). It worked nicely.
Last year, I made a new one with a totally different cluster set-up. Two C6's, mounted skewed so that their thrust not only provided upward thrust but spin thrust. There are three photos of it on the BRB website:
https://birminghamrocketboys.com/BRBGallery/July15,2006Launch?page=1
The last pic shows it descending after burnout.
Also see pages 2 and 4 for liftoff pics showing it taking off, with the angled exhaust smoke.
At NARAM, Chris Taylor took some video of it. The video showed that the model did not start to spin until it was up around 50 feet or so, and it wobbled a lot as soon as it left the rod. That explained why it did not fly take off as gyroscopically smooth as my previous rocket Frisbees had. That model often ended up angled off a good bit and after apogee it often glided at a steep angle. So, I have not flown it since NARAM. The reason why it did not spin up much in the first 50 feet is the leverage of the skewed cluster mounts, being concentrated near the center. Those same skew angles at the rim would make it spin pretty quickly at liftoff, but the aerodynamic drag of nearly perpendicular engine mounts near the rim would have killed the glide in descent, and the centrifugal force at the rim would make it very likely the mounts would break off.
So, the best ways to do Rocket Frisbees are to either use a mechanical spin platform, or cluster a mini-engine on the rim to spin it.
Thee have been some full-sized sounding rockets that have used spin motors. Check these links for some X-17 info:
https://designation-systems.net/dusrm/app1/x-17.html
https://www.astronautix.com/lvs/x17.htm
- George Gassaway