Flywheels work perfectly well when used correctly.
You can't run a car with one, but you can use it as a hybrid, either a full hybrid or a patrial hybrid. It's also not worth tapping energy from a flywheel with the method you described, it's best to either stick it into a generator or use a CVT pully.
see:
http://www.flybridsystems.com/
Vehicles produce a good proportion of CO2 when pulling away, the idea of partial hybrids using flywheels is that they provide the power to pull away so a few HP for a few seconds. Which can give a decent saving for CO2/km on the duty cycle.
For storing high amounts of energy we need 2 things:
http://en.wikipedia.org/wiki/Rotational_energy.
1. A high J value. (Angular mass).
High angular masses mean more energy is stored per RPM. It also means that the outer edge of the material stores the most. This means we want out flywheel to be like a doughnut.
However from the power equation we can see that w^2 vs J. This means rotational speed is actually more important than J for achieving high energy storage. The angular speed increases stress on the flywheel, so we want to make it out of something with ver high strength but low weight. It's why we make them from carbon fibre.
2. High rotational speed.
High speeds, means that the flywheel needs to be run in a vacuum for efficiency. This is obviously difficult if you need to attach it to a shaft to tap the energy. So one of the areas of development is a magnetic coupling (essentially a fixed magnetic gear ratio).
http://www.ricardo.com/en-GB/News--...nd-generation-high-speed-flywheel-technology/
http://phys.org/news/2011-09-flybus-prototype-hybrid-bus-future.html