THis doesn't seem feasible at all. How much light from the flash if going to strike the photodiode? 0.001%, 1%, 10% etc? It will be different depending on where the photodiode is placed. Moreover, you're also going to integrate a greaty deal of background light, unless you perform this in a darkened environment, or have a shutter exactly timed to the duration of your flash (you'll still integrate background light doing this, but not so much assuming the light from the flash incident on the diode is many times the light power of the background).
To calculate the power of light incident on the diode is fairly easy, you just need to know the area of the photodiode and the quantuim efficiency etc. which will be given with the data sheet. That will only give you the power of the light incident on the diode though, not the power odf your source.