If the diode is in place, there is no flyback voltage above the forward drop of the diode. The initial diode current is equal to the current that was flowing in the inductor before the current was interrupted, e.g., if 1 Amp was flowing in the inductor, 1 Amp will initially flow through the diode before the current decays. This fact causes diode-snubbed relays to hold on for milliseconds after they are switched off.
Without a diode, the peak flyback voltage is mostly a function of the inductance and parallel capacitance (generally interwinding capacitance), unless breakdown occurs. Keep in mind that v=L*di/dt, where di/dt is the rate of change of the current. If the current goes to zero in essentially zero time, v can be huge. Shunt capacitance will absorb the current which wants to keep flowing. The larger the capacitance, the lower the peak voltage. Of course, if the inductor has fairly high Q (low effective series resistance), prolonged decaying ringing will occur at the resonant frequency of the LC circuit.