Welll.. empirical measurement would be your best bet.
Keep in mind that the flash write takes some amount of current over a period of time to write fully, thus a total "charge" used. But, current draw drops voltage, and if the voltage drops too far, then the chip will power off, reset, or behave erratically, thus the effective point at which you can write to flash would be at a higher recharge state than you might think. The flash requires higher CPU speed however, which will draw faster current for sure. At a guess, I would say 25+ mA of current would be drawn when writing the flash, but I am guessing at this point.