The basics are no flying of any kite above 200 feet (60 meters) above ground level or 30 meters in the vicinity of an aerodrome/airport. Vicinity means roughly within 2 miles of it's boundary.
Unfortunately it does not end there. Although the following may seem a little nerdy, it does unfortunately exist. That said I do not know of anyone in recent times that has been prosecuted under the Act. I am referring to the Police Town Clauses Act 1847 (England only). This effectively bans any kite flying in any public place or highway that may cause undue distruption or distress to humans or animals. This is important because large noisey kites can cause severe distress to animals. Horses can shy, cattle and sheep stampede. Furthermore in the lambing season around us in the Peak District there are restrictions in force for public activities to avoid undue distress for the ewes. So you have been warned, please be considerate in such circumstances.
The information here is only applicable to UK air space.
Please consult your own countries Rules of the Air and any Air Navigation Orders that are in place.
Download the CAA KAP Permit form from: HERE