I live on the cost close to the islands.
If you mean Ponza, Palmarola and Ventotene, then I've never seen a kite beach there.
Actually it's more about rocky spots and beaches are covered by cliff. So I don't think you'll find good options to lunch your kite from the ground.
Also, kiting is banned during the summer and restricted to allowed areas only.
Why don't you lunch by the boat tender instead ?
By the way, those islands are very nice and going with your boat is the best option to visit them.
Don't forget your snorkeling equipment ! This is great Scuba diving spot.