I have a few kites....they are mostly stored rolled up in sleeved and bagged together with their family.
There are some single line kites that never break down fully, this could be intended (Scott Hampton Cypods always have their leading edge rods in so the painting is flat) or unintended (Fridolin Anders Frido II that are framed with a single looped piece of carbon)....I keep those out of extreme temp or humidity.
edit:Bags are laying flat on a shelf system btw...
That is one thing that many people do not think of: humidity.
Great example is Ramal Tien of L'atelier. His workshop is an old mill building over a river. We had gotten in a bunch of his Sentinelle kites (long white three winged and highly tensioned single lines) and in the winter when the humidity was low, or the one that we shipped to Nevada, twisted up like a rotini pasta. The skin shrank so much due to the humidity.
The kite that went to Nevada had to be forced assembled after being showered and then left assembled for a week or so to let the skin stretch a bit on purpose....
Some kites like a Photon fighter are pretty flat and have weird framing....i have a couple of those hanging on the wall as it is a safe place and they look cool too....
Nice! I've been thinking about hanging some from my vaulted ceilings to have that kite shop motif going.
I have a piece of board on my closet shelving since the shelving has those wiring style and spaces. For the taller kites I have them standing on end.
None of them are connected to any elastic cords for the LE such as with the Zephyr etc. I leave them all loose. Only ones I keep snug are really the Prism kites that have the velcro straps that came wrapped with them. I'm debating even loosening those too.