Eh, it's always been my understanding that the problem with rocket packs (and by extension, this) was fuel. Wingless flight -- and believe it or not, helicopters are "winged" flight, which is why they can "glide" (autorotate) -- requires insane fuel consumption.
Someone figuring out how to strap jet engines to themselves and not instantly die is impressive, but it's not really solving the hard problem. The "10 minutes" claim is probably already based on loading up with the maximum amount of fuel the person can carry - add more and you don't get off the ground without adding another engine, which burns more fuel...
So I find the claim totally believable, and impressive for what it is, but it's not the sort of thing that has me reaching for my wallet to throw money at the guy.