The main issue with a jetpack is the amount of energy needed. No practical jetpack or rocket belt has ever been demonstrated which can carry more than a few minutes worth of fuel. Jet and rocket engines are notoriously inefficient in terms of fuel consumption, which simply adds to the problem. You will notice that modern jet aircraft have moved away from turbojets to turbofans, where the turbine turns a large fan to move a large mass of air somewhat slowly (while the internal jet engine moves a smaller mass of air very quickly). The larger the bypass ratio, the more efficient the engine.
Taking this to the logical extreme, we go to "unducted" turbofans, or turboprop engines, but you are probably not going to be too keen on having large fan blades or a propellor whirling just over your head...
The only practical way to overcome the limit is to have a beamed energy propulsion system, where a powerful laser of microwave generator on the ground provides the energy to a target on the backpack. While there have been serious proposals for this idea applied to helicopters, aircraft and even rockets, you can imagine the issues with that system scaled to a man portable backpack....