Typical flash lamps need >170 V to operate. Fortunately, the operation is based on discharging a capacitor; the discharge duration is short, some 20-50 ms while to charge the capacitor, the power supply has a longer time.
My advice is to find a DC-DC converter capable to charge the capacitor to >180...200V. If you can modify the existing circuit, use a voltage multiplier with diodes and capacitors to get more voltage. Maybe the original circuit has a bad diode or capacitor. Also test the charging capacitor, some can leak and overload the power supply. Be very careful, a charged capacitor is dangerous at 10-100 uF, ~200 V. Also the DC-DC converter is dangerous due to high voltages in it.
The triggering circuit develops up to 5 kV pulse, also dangerous to touch!
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What is the AC input voltage, V1? If it is 120 V AC, then the full voltage in "141" capacitor will be ~150 V. If you use a voltage doubler, you can get up to ~300 V DC. Then the capacitor may fail- check if it can hold 300 V.