UT Austin's cannon-caliber railgun had some impressive pulsed-power output from flywheels for demos (a 150g projectile launched at nearly 2km/s), but they were fired a single-digit numbers of times.
It would seem that flywheels can store a lot of energy, but due to the form of the energy storage (kinetic) it’s difficult to discharge the current quickly, so to speak. Especially compared to something like a capacitor which is designed for rapidly discharging a literal current, as opposed to the analogous metaphorical motive current in a flywheel.
The flywheels GP refers to were homopolar generators [1]. They created an impressive current pulse, and extracted almost all the kinetic energy in less than one revolution.
Yah, that's a railgun, but it's not what everyone around CEM called the railgun.
The difference being one between a .50 caliber machine gun and something that can sink a ship from 100km away.
I worked across the street from CEM at the time. Firing the railgun was a big deal. The mechanical stresses on the electrical systems were pretty severe.
The vast proportion of what UT CEM was doing in that era was with the big gun, for Navy and SDI type projects.