Ok, so based on the energy requirements specified here(see entry "20060102"), and assuming you would actually want to keep the outer edges of the flywheel subsonic, I'm getting a mass of at least 312000000kg. To make a flywheel that big out of an average steel alloy (with a density of about 7700kg/m³), it would need to have an outer diameter of 333m, an inner diameter of 313m, and a thickness of 4m. At that speed, it rotates about every 3.5 seconds.

So what we have is a massive steel ring, roughly as big around as the length of an aircraft carrier, spinning at near the speed of sound. Sounds completely workable. Yep, no non-trivial enginnering problems there. Nope.