Minimum Current for Zener to Clamp Vgs of Mosfet?
The information is in the datasheet, you just didn't know it.

The MMSZ5221BT1 has a Zener voltage of only 2.4V nominal.  Its likely that the FET won't turn on at that gate voltage.  If you want the max gate voltage to be 16V then you need the MMSZ5246BT1G.

The big table on page 2 gives you the info you need.  IZt the Zener current in the column heading is the test current (7.8mA in this case) for establishing the Zener voltage Vz (16.8V max).  IR is the maximum current (1uA) at test voltage VR (12V).

From that info we know that the diode will draw 1uA at 12V and 7.8mA at 16.8V.  So if your diode current is between 1uA and 7.8mA then the diode voltage will be between 12V and 16.8V.

If you are just using the diode to protect the gate then the exact voltage won't be that important as long as it significantly above the gate threshold and well below the max rated gate voltage.  12V to 16.8V seems like it would be.

From practical experience I would bet that at 200uA the Zener voltage would be very close, but a little below 16V.