Hydrogen peroxide powered rocket packs fly for around 30 seconds, because they have a specific impulse of around 125, meaning that one pound of propellant can make 125 pound-seconds of thrust, meaning that it takes about two pounds of propellant for every second you are in the air. Mass ratios are low for anything strapped to a human, so the exponential nature of the rocket equation can be safely ignored.
A pretty hot (both literally and figuratively) bipropellant rocket could manage about twice the specific impulse, and you could carry somewhat heavier tanks, but two minutes of flight on a rocket pack is probably about the upper limit with conventional propellants.
However, an actual jet pack that used atmospheric oxygen could have an Isp ten times higher, allowing theoretical flights of fifteen minutes or so. Here, it really is a matter of technical development, since jet engines have thrust to weight ratios too low to make it practical. There is movement on this technical front, but it will still take a while.