Yes, I am a former falconer. The regulations depend on your state.
Falconry is regulated at both the federal and state level. At the federal level, birds of prey are covered under the migratory bird act. At the state level, falconry is covered under the fish and game regulations of the state. So… bottom line is you apply for a license through your state which is in turn signed off by the federal government.
I can ramble on about the regs and requirements in the state of Texas if you wish, but the short version is there are three levels, you start as an apprentice and must have a general or master falconer as a sponsor, after two years you can get your general license, after a couple of years as a general falconer you can get a masters license. Each level carries with it differences in the number and type of birds you can keep along with privileges to sponsor apprentice falconers. You really need to contact the fish and wildlife department in your state to find out how they do things.
From a practical standpoint, be advised that it is a very labor intensive hobby, and if you are just interested in taking a passing interest or simply want a “cool” pet, falconry is not, I repeat NOT for you. You will need to spend at least an hour a day with your birds and you will need to have the location/ability to take them out to hunt at least once a week.
Kestrels are fun birds to have, but more difficult than you might think as falconry birds. In falconry, weight is everything, and controlling the weight of such a small bird is challenging. Additionally, their prey are things like field mice and not exactly fun for we humans to hunt. A red tail is great for rabbit hunting, but there is nothing like hunting ducks with a peregrine!
Anyway, good luck in your endeavor, but please don’t take the responsibility lightly.