Capacitor and discharger selection for pulse discharging
If the flash lamp will handle the power, your unit should do the job. However, you need a much bigger capacitor.

As you've calculated, 100 joules in 350 usec is 285 kW, assuming constant current and voltage. At 1 kV, this is a current of 285 amps. the nbu max is 1000 amps for pulses less than 1 msec, so you're fine there.

However, if you've sized the cap so that its energy is 100 joules at 1000 v, it will be completely discharged at the end of the pulse, and so the current cannot be constant.

Let's say you want the capacitor voltage to be 1000 volts at the beginning of the pulse, and 900 volts at the end. That says that your capacitance needs to be about 1000 uF. 

Also, as you know you need to find the flash equivalent resistance. In order to get 285 amps at 1000 v, you need an equivalent resistance of less than 1000 / 285 ohms, or 3.5 ohms. Allowing for stray resistances in the wiring and the nbu, you'll need a maximum flash resistance on the order of 2.5 ohms. Any more and you'll need a higher voltage on the cap, and the nbu won't work.