Flywheels are a short term energy storage technology. Mostly used for voltage control and emergency Uninterrupted power at hospitals, computer centres, etc.
No one is looking at big cheap flywheels for day night grid storage but that should work if you can make it big and very cheap. Those working with flywheels to date have focused on high speeds. Energy density increases exponentially with speed but so does structural stresses and thus cost. Energy density increases lineally with mass but with concrete and steel the cost decreases with size and mass. Someone needs to look at whether really big wheels, what I call "millstone flywheels" would be viable.