Time to accelerate up to motor speed using the rated motor torque...
Torque = Moment_of_Inertia x delta_omega / delta_t
Transposing..
delta_t = Moment_of_Inertia x delta_omega / Torque
= I_flywheel x angular_speed_from_zero / Torque
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Where:
delta_omega = change in angular rate (e.g. starting at zero).
delta_t = change in time in seconds
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Use these slightly different formulae to get the time to accelerate the fly wheel up to the speed.
Torque = I x Alpha
transposing..
Alpha = Torque_N.m / Inertia_kg.m.m
Time in seconds to get change in speed in radians per second
= speed_radians/s / Alpha
Where:
Torque in N.m
I = Moment of Inertia (kg.m.m)
Alpha = Angular Acceleration in radians/s/s
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In practice the torque also has to overcome friction of the bearings and any gearbox. Obviously the gearbox is set to adjust from the motor rated speed to the highest speed of the flywheel. This changes the torque, so if there is 3:1 reduction, the torque is 3 times, less the loss in gearbox efficiency. Make sure the gearbox is rated accordingly at the output shaft. So after this gearbox it could be 60% of 3 times the torque. Allow for additional starting and pull-up torque if you are using them. The VFD can be constant torque up to a speed I expect. The additional friction for flywheel bearings and windage? Well you can just set to the motor rated current or a little less, and accept how long it takes after estimating as above. That is all a given motor can do. Watch the cooling if the motor runs long with low fan speed. You could attempt to measure bearing friction by the motor mechanical power needed to run at some fixed RPM. This would be like 80% of motor voltage x motor current considering power factor. The VFD might provide this figure.
The time to accelerate will always be longer than the results calculated above, because the motor and drive train inertia, friction and wind losses all contribute to a longer acceleration for a given torque. The accuracy depends how much trouble you take in allowing for these factors.
You could also measure inertia with drum and weighted cord, to determine acceleration for given torque and period.