Actually I gave you the part number for a Triac which would work, but an SCR would probably be better. An example is the Littlefuse S6008LS3 which is rated at 600V and 8A.
The minimum anode-cathode current for the SCR to stay on is IH on the data sheet, which for the S6008LS3, is 8mA at room temperature. If the current drops below that the SCR "may" reset to the off state. To insure reset, the current should probably be less than 1mA.
The gate trigger current for this device is 0.5mA minimum. A good value to insure triggering would be 5-10mA so select a gate resistor to give that current. The gate looks like a diode with a 0.8V maximum (~0.7V typical) gate-cathode voltage at room temperature.
The gate pulse should be fairly short so that the SCR doesn't stay latched on by the charging current after the flash fires. The typical required gate pulse is 5us so 50-100us should be adequate.