Power mosfets can tolerate absorbing a certain amount of energy in avalanche mode (without any clamping or flyback diodes). Look at the figure on the datasheet for repetitive avalanche energy, in the absolute maximum ratings section. In practice, this typically means you can use an unclamped power mosfet to drive a small transformer, but not a large motor or solenoid.
if you use a self-clamping zener between gate and drain, then the energy from the inductive load is still dissipated in the mosfet. The difference is that the mosfet is operating in the linear region, not the avalanche region. There will still be a spike in the die temperature. Whether the energy it can absorb in this mode is greater than the maximum avalanche energy is difficult to say - I've not seen any figure given for maximum linear mode energy burst given on a datasheet, nor on the thermal capacity of the die. So this arrangement is not a generic substitute for a flyback diode.
If you connect a flyback diode across the inductive load, then the flyback energy is mostly dissipated in the inductive load, with a little dissipated in the diode. So no worries about the energy-absorbing capacity of the mosfet. The disadvantage is that the current in the inductive load decays more slowly, which can be a problem in some applications.