What Wattage does my resistor need to have to be save to dim an LED strobe module?
I take it you measured the voltages.  The current was probably and assumption.  You can solve this just using voltages.  Formula is V^2/R.  So you have 100/500 Watts.

Something seems wrong with your numbers however.  This would also imply that 20mA.  Are you sure the value of your resistor isn't 50 Ohms?