The economics of flywheels for this kind of application versus just using another battery tend to rest on the purported "unlimited cycle life" of the flywheel system compared to, say, Li-ion batteries that have a very well documented finite cycle capacity that degrades even further when doing sub-optimal cycling. To a lesser extent you can also bank on lower parasitic loads during standby as the environmental requirements for a flywheel aren't as stringent as batteries that need to be either heated or cooled almost all the time in many climates.
The problem is that, by and large, "unlimited cycles" is not true. You still have huge, very high speed bearings. Motors that require routine electrical testing and can fail. And now all this stuff is sitting below ground under a massive concrete lid for containment so it's not as easy to do maintenance on compared with a similarly-sized battery system. You also need uninterruptible power supply to maintain safety and control systems when grid power is unavailable since you've still gotten a huge spinning mass that you can't slow down without somewhere to send the energy (it's possible to use braking resistors, but it's another cost).
Batteries also benefit from massive economics of scale (both on the actual cells and the power electronics) that are getting better with time and driving costs down, while flywheels have been "1 year from commercialization" for the last 25 years.
I remain skeptical of the commercial benefits vs. increasingly commoditized and readily available battery systems.