The order is able to fly due to the high tech suits that have been created for them to use. Both Stealth and fight suits have existed for quite a while now and this is the reason why members of the order are able to do so many things and move around freely without even being picked up by the most advanced radars available on earth.
There is no doubt that this is the kind of invention that will create a huge revolution once we allow it to go commercial, but we do not see that happening for the next 50 to 100 years at the very least and depending on many factors. Stealth camouflage and flight suits could be extremely dangerous it if falls in the wrong hands and we want to make sure that we release it at the right time. There is nothing more important to us than to be able to keep these inventions hidden from the public for a while.