The diode only needs to handle as much speed and current as the transistor doing the work. Flyback isn't some magical surge, it's merely the continuation of whatever current was flowing when the switch opened.
Accordingly, the diode should also be placed
at the switch, diverting the current into a stable (locally bypassed) supply.
It's not the coil that's making the flyback, it's the switch. The coil is just a reserve of EMF (voltage). It's the switch (and diode, and whatever else in the circuit: resistance, capacitance and all that) that causes the waveform.
Tim