To be honest, I suspect the peak power was higher than stated. Assuming the flash cube is the old resistive type (the newer mechanical ones shouldn't have gone off at all), and takes at least 3V to fire, that's only 66mA peak current at 200mW.
Unless the induced voltage was still high enough to light off a small spark / arc somewhere along the metal, which would almost immediately ignite it. Who's up for some flash cube vs. amateur radio transmitter "experiments"?