I assumed that with brushed motors, when the field collapses (creating reverse induction) the brushes have already moved on from the energized coil and set of contacts on the commutator and had moved on to the next set. By this time isn't the electrical connection broken, preventing the induced current from heading back through the communtator & brushes
The individual armature coils are connected such that in effect the whole thing is one big endless coil; the commutator switches "taps" rather than disconnecting anything.
You could try a bridge rectifier as a "clamp", the AC side to the motor and the DC side to your DC supply, before the relay contacts.
That's not quite a flywheel diode, but any voltage spikes greater than supply voltage get absorbed by the main supply; justy make sure that is reasonably low impedance itself - eg. add a capacitor across it, at the bridge DC output.