This is totally wrong. You need at least the normal worst case (locked rotor, or whatever limited by current limiter circuit, if any) motor current draw, simply because the full motor current goes through the diode.
Well. This is totally wrong, because the diode is pulsed, not continuous.
Except for the very smallest of diodes, the pulsed rating is always very favorable. Example:
https://www.onsemi.com/pub/Collateral/MMSD4148T1-D.PDF200mA average, 1A surge (< 1 s). It's unlikely that flyback would last that long, so you can use the thermal profile (if provided) to determine exactly how much is tolerable for other pulse width and duty cycle.
In short, the diode does not need to be any larger than the switch delivering that current in the first place. Whenever I see 2N3904 driving a load with a 1N4001 across it, I'm amused. 1N4148 is more than sufficient there. Now, 1N4148 would be inappropriate for a TIP120 or IRF540 switch, say, where a 1N400x, or even better still, UF400x, would be appropriate.
A zener/TVS can also be used, which has the advantage of faster discharge time (faster relay and solenoid operation) and returning the current to the switch's common terminal (GND), protecting the switch.
Note that the flyback diode should be similarly returned to common, NOT placed directly across the load. This is unimportant for short lead lengths, but an exaggerated case -- say, many meters of cable between switch and load -- introduces stray inductance, which is the very thing you're trying to deal with in the first place. Note that, in this case, "common" means AC ground -- the exact "common" you would use is +V, bypassed to GND (or switch common) with a large enough capacitor, at the switch. Thus, when the switch turns off, the current flows from the switch, to the diode, through the capacitor, back to the same common. This loop being physically small ensures minimal stray inductance, and thus overshoot voltage at the switch. This principle extends to proper switching converters, where it's done at scale, and overshoot is a necessary consideration.
Tim