How to calculate secondary RMS current of each winding in multiplre output flyback converter?
Wire gauge is determined by the required output current.  Estimate the wire length from the core size and number of turns, the calculate the resistance.  Remember that the resistance of copper is a function of temperature, so you can use the wire resistance at your expected transformer temperature.  The wire resistance is in series with your output, and you can perform the R*I^2 calculation to determine the power you will be generating which will be both a transformer loss and a heat source for your design.  Remember that you will be supplying pulsed current, so your voltage drop will be greatest immediately after switching off the primary, and the voltage must be high enough immediately after switching.

You will have to do some math.  When your power supply is fully loaded, what is the duty cycle?  It depends on whether you are in discontinuous mode or continuous mode and the duty cycle, but the peak current on the output winding will be much higher than the average current.  It should be relatively easy to draw a theoretical waveform, and then calculate the result of adding the expected winding resistance.