I really enjoyed this video about how to use a Flywheel Braking System to store energy, and then use that energy when you are ready to resume cycling. The storage of the energy only amounts to 15 to 20% return on the energy stored, but also comes with the added weight being carried around, and the noise caused by the gears/flywheel.
So the amount of energy being stored and used doesn't really seem worth it when you consider the problem that the cyclist is carrying around all this extra weight, but only using that weight to their benefit when braking and restarting.
So yes, an interesting experiment, but ultimately it makes you realize that it isn't an efficient way to do it. Plus the noise... Just not worth it.