Interesting approach, though I don't take the flywheel thing for granted. The way they are described, they will not counteract lateral displacement, so the wind will still make the whole thing sway, probably enough to affect its integrity. Unless they come up with significant improvements, we're not going to see this in reality.

A rocket is inefficient mainly because the exhaust is usually moving far faster than it needs to, as well as "carrying everything." What you want at 12 miles high is enough speed to actually need a rocket, or you have only avoided a little bit of air drag. The atmosphere can, however, provide both fuel and lift to the first stage or two of a space shot. We'd be a lot farther ahead using Jumbo Jets harnessed together to make a giant glider tow to pick up a scramjet 2nd stage from a fast truck.

Nice if it would work. But getting up into the jet stream and it's potential tornado force winds would tear apart any man made building. The idea of landing on it would also be unlikely. The air would be so thin that any parachute would have to be huge and anything flying would have to be able to handle high velocity winds and the ability to fly slow enough to land in extremely thin air.

I had a similar idea but, my idea didn't have to support all that weight or land anything on it. My thought was to use regular weather balloons to support a tube and cable design. That a solar cable walker could climb inside of. Where stability and wind speeds become a problem the tube would end and a flying cable with wings would takeover. The wings would be computer controlled for zero weight and stability (similar to a kite). The number one problem with high altitude elevators is weight of structure. Which could be mitigated by Balloons and wings. That way you don't have to wait for carbon nano tube production (I have another idea on how to speed that up as well). Back to the cable, this could extend at least 40 miles and could reduce weight and cost of delivering costly space supplies like water and fuel. The walker would carry a small missile sized rockets. There's no reason you couldn't launch 50 a day. That would reduce the costs about 80% for small mundane supplies to space. Also reduce pollution by 9999%Once at the top the rocket would be thrown away from the structure prior to ignition. The savings of the structure to fuel weight would limit the size to only being able to carry liquids and nano devises. The average cost of taking one gallon of water or fuel to space is $10,000 from what I've heard. If you can't launch 10 gallons for 10 to 20 thousand per rocket then your scientist are worth a hoot. But, I'm only a fire fighter and dreamer. I see people doing things wrong all the time it just frustrates me. I would like to point out that your design is most likely for orbital skippers. However, the speed of those aircraft would incinerate your elevator design. P.S. if you can't put this to use then can you pass it on to Elon Musk I'd love to work for him.

They've reinvented the Short Stack!
(From one in a series of SF short stories about an inventor named Short.)

martinkopplow, The speed of rocket exhaust is called the specific impulse, and it helps to determine the thrust of a rocket. The faster the Exhaust, the greater the thrust.
I agree with you about using the atmosphere on the first stage, as the oxidant for fuel (liquid hydrogen.)
A horizontal takeoff, with some sort of catapulted or electromagnetic boost would also save fuel.

Unfortuately, make a start of the space rocket 20 km higher will not make any significant difference in fuel savings.
http://space.stackexchange.com/questions/744/effect-of-atmospheric-drag-on-rocket-launches-and-benefits-of-high-altitude-laun

My idea, is not to even try this foolish idea. and maybe spend, what no doubt is tax dollars, dreaming up half baked crap like this.

Why not send everything up in a giant balloon and go from there?

The novel idea here is a lighter than air building. The overpressure of the 100 mph jet stream is about the same as 50 mph at sea level. The jet stream coud also provide lift to support the building. Vehicles could be launched downward from the building. Or through a tube with the top open to near vacuum and the bottom at sea level. The doubling length ( at 1 g ) of S-glass is 20 mi.; carbon, 60 mi. The space elevator needs active stabilization, such as rockets.