What's the purpose of the MOSFET on the output of the flyback buck converter in this circuit?
It's acting as a synchronous rectifier. See the body diode I've highlighted in blue: -
ThatBy itself, the blue diode would beis how you would place a regular diode in the circuit. The MOSFET replaces the regular diode and, when expected to conduct, the MOSFET shorts out its own body diode giving lower conduction losses than a regular diode.