You shouldn't need one since you aren't doing high frequency switching the motor. Putting in a flywheel diode means you will have to mind the polarity when you hook up the motor to the mains and will just reduce the arcing when you shut the motor down which may be desirable and make thing less scary.
If you raid a smps for its bulk cap also raid the Ntc thermistor, big caps esp low esr ones in smps's can take out a breaker or short the rectifier on power on.
Plenty of older Dc industrial drives do not have a bulk cap, the motor will hum a bit without but it should still run fine.