Basic 'flying suit' ?
Well, there's the classic 'jet pack', running on 'HTP' H₂O₂ mono-propellant. Upside, flown on 'James Bond' and, in real-life, lit Olympic Stadium flame.
Down-side(s), 'HTP' is *seriously nasty* and, IIRC, less than a minute flight time...
I've seen a 'jet suit' with four mini jet engines as developed for *serious* R/C models, one per arm & leg. IIRC, flight duration is 'good' but control '
A Tad Fraught'.
Quad/Hex/Octo copter drones now have sufficient lift capacity and useful range, so ducted fans may apply. Uh, aren't Ukraine trialling them for 'Medevac' ??
So, are you going for electric power plus ducted fans ? Jet engines ? 'Combustion' Rocketry with mono or multi propellants ? 'Thermal' Rocketry with electric power plus inert propellant ?
A possible contender is valve-less pulse-jet, those 'flying trombones' with resonant pipe. Upside, the things work and have remarkable power/weight. Down-side, they are really, really loud. Totally anti-stealth. Yes, they also run red-hot, but I suppose you could fit them with a 'muzzle shroud', heating of air within shaped duct providing 'negative drag'...
On the 'gripping hand', pulse-jets exhibit 'bad vibes' without sufficient vehicle 'fly-wheel' mass. IIRC, the scant-few V_1 test pilots had *unkind* things to say about that aspect of their ride...
Taking a leaf from young field of 'Pulse Detonation' jet engines, if several valve-less pulse-jets could be co-ordinated to fire as a three-stage multi-vibrator, a 'flip-flap-flop', ride may improve.
Obvious analogy is the magnetron with its 'linked' resonant cavities...
Perhaps as 'after-burner' for small fan-jet, with compressor-bled 'puffer' air for flight control, while fan blows, cools the 'muzzle shroud' ??



