Why ? They don't need to be synchronized at all, as long as they're roughly spinning at the same speeds in opposite directions there is 0 effect. The only effects you'd be left with would be from the difference between the two rotational speeds. If you stop one and the other continues that's a different matter.
Besides, keeping two wheels synchronized is not the hardest thing to do, a car contains a lot of moving, synchronized parts.
Flywheels running at high speed are not made of cast iron or other things that turn in to 'shrapnel', they're made of wound filaments of carbon fibre bound with resin, usually they are designed with failure in mind. The bigger problem is dealing with the conversion of the energy in the wheel in to heat.