What is the purpose of a schottky/zener couple on an isolated flyback topology?
They are there to avoid over voltages on M1. 

These can easily happen due to “leakage” inductance in the transformer.

No transformer is ideal so, in addition to the excess voltage when the transformer is discharging into the secondary, any current due to leakage inductance must also be discharged somehow. 

Due to the needed excess voltage for normal operation of the secondary, the zener becomes necessary. 

Depending on how much leakage inductance there is, it is possible to simply add an RCD snubber to dissipate the energy. But a zener and a diode is much easier to calculate.