Every vehicle that I have ever read about that used a flywheel for energy storage coupled the energy in and out electrically. That seems like it would be the most straightforward way to do it, because it would be very easily controllable and there would be very little loss.

Also, most of the flywheel concept vehicles I have read about used multiple flywheels, spinning in opposite directions, so that the precession effects would cancel out.

The biggest challenge actually appears to be safety. If you get in an accident, those flywheels are not going to just stop spinning. If they have a lot of energy stored in them, think "Tasmanian Devil". Much of the work has been focused on making enclosures that can contain them in the event of an accident. It's also an argument for making multiple, smaller flywheels, as opposed to a couple of bigger ones.