Bell & Williams did that back in the 1960s
when they fitted the Williams WR-19 turbofan engine to the rocket-belt idea. It flew well and had an anticipated endurance up to 26 minutes. They even developed some more capable versions that didn't depend on the pilot's legs to dictate maximum vehicle weight. I've always wanted one of those, even if they were probably too noisy for city use.
So, while the idea isn't new, I wish the new guy well.
I LOVE the quote at the top of the linked page. It should be tattoed on the arms of tort lawyers.
Insisting on perfect safety is for people who don't have the balls to live in the real world.
- Mary Shafer, NASA Ames Dryden