According to my hand calculation, the secondary winding losses are almost negligible. But the core is driven into saturation, resulting in huge losses.
Are you sure about the secondary wire size?
Do you mean 36 AWG instead of 26 AWG?
With primary 10T of 21 AWG and secondary 86T of 36 AWG, the fill is already 96%.
According to my hand calculation, the secondary winding losses are almost negligible. But the core is driven into saturation, resulting in huge losses.
The first step is to calculate the true rms currents from the expected triangular current waveforms.
DCM flybacks are notorious for having very high current peaks, with short narrow pulses that produce extremely large crest factors.
The average output of 200 mA sounds harmless enough, but the current peaks can be many times that, and the true rms current much higher than expected.
Try to keep your conduction periods as long as possible using all the available time at maximum load, and at minimum input voltage, by not making the air gap any larger than absolutely necessary.
Also be fanatical about skin effect, it will make a much bigger difference where very high crest factors are involved. Reducing the switching frequency may be an option ?