If we stick with one of the very common readily available 100uH toroidal chokes, and we turn on the mosfet for 30uS the current will ramp up to 1.5 amps (with 5 volts applied).
That will store 112.5 microjoules of energy.
If our switching frequency is 30 Khz (33.3uS) that will be able to ransfer 3.375 watts, assuming no losses.
So the choke charges up for 30uS and discharges into the output for 3.3uS, which it will very easily do.
The input current will average out at about half the peak, or about 0.75 amps.
That should just get you 10mA at 300v.
See how you go with that.