what I really want to know if he ever finished his scooter!

It would be legal to run it on the factory engine, at which point the jet is just cargo. If you start the jet on a public road, it could be considered a public nuisance, reckless driving, etc.

If a the vehicle presents a clear and present danger of any kind it is a-priory a ticketable offence at least. With the jet off, it poses no such danger.

I'm certain an officer could find all sorts of reasons to ticket that vehicle if inspired.

You can own a car, you can own a flamethrower, you can't fire your flamethrower out of your car while driving on public roads.

And for California, don't forget "Exhibition of speed" which is a rather nasty ticket to end up with.