Power of the Zener diode
I think you have to consider two situations. In discontinuous conduction mode the entire energy in the inductor (ideally) gets dissipated by the zener each off period. 

The current in the inductor increases as i(t) = tV/L , so the energy at the end of the charge time \$t_{ON}\$on is 

E= \$\frac{t_{ON}V^2}{2L}\$

In continuous conduction mode there is still some current flowing in the inductor at the end of the off period, so the current increases linearly from the initial current and the energy that goes into the zener is proportional to the differences of the squares of the initial and final currents. So in steady state there is some constant amount of energy stored in the inductor at the  end of each off time.