Re: small issue of air density
The fun thing with Dyson patents is to look at some history. A century or so ago, vortex separation was used in coal mines. Over three decades ago vortex separation was used in bus exhausts to reduce particulate emissions. There was a vortex separator at a sawmill where I worked long before Dyson invented the vacuum cleaner. Like everyone else involved in technology, I do not look at patents because they are obfuscated, obvious, describe antiquated tech badly and looking at a patent means triple damages for wilful infringement (and expensive nuisance litigation if you do something similar but non-infringing). So without looking at Dyson's patents:
Flywheel energy storage has been around for decades. The big advantage is the rapid discharge time, so to obvious uses are things like throwing aircraft off a carrier or powering a data centre for the few seconds between a power cut and the generators starting. There was a big step up in capacity per kilogram when people switched to composite materials. In 2004, NASA built one that could store 16kJ/kg. For comparison, super capacitors store 36kJ/kg, Lithium ion battery: 1800kJ/kg. Ham and cheese sandwich: 10130kJ/kg. The popular energy storage for a Mars rocket is Methane+Liquid oxygen which you can make from Mars's atmosphere if you bring a nuclear reactor and your own hydrogen. The resulting energy density compares well to a ham and cheese sandwich, so over 600 times better than a flywheel storage device built with an astronomical budget; eg: launch costs per kilo swamp the costs of expensive materials and expensive manufacturing processes.
If you are going to try flywheel storage for a Mars landing, the time to charge up your propeller is after you have slowed down enough that the propeller will not get vaporised by friction with the atmosphere, but while you still have enough speed and altitude for autorotation.
If Dyson were involved in space travel, I expect he would patent what other people are doing now and sue them when they start to make a profit.