Unfortunately, Stapledon gave little info about how it was supposed to work.
Flight is our ordinary means of locomotion. A man has but to put on a suit of overalls fitted at various points with radiation-generators. Ordinary flight thus becomes a kind of aerial swimming.
Could this idea be made real with our current technologies? Flying cars are coming soon, and it's easier to make a person fly than a car. So it doesn't seem a far-fetched idea.
Last Men's suit would be way more convenient than a flying car. Flying cars would still need to park, and cities are already crowded. A suit can be put in a wardrobe when you don't need it.