I had the brilliant idea of putting my orthotics in my wetsuit booties to try and overcome the pain of kiting with flat feet,
didn't work, actually made it a lot worse.

anybody else with flat feet come up with a solution?

i have super flat feet and have never had orthotics. Just don't do your straps/boots up too tight. usually i just need to warm up for a bit then they come good. no complaints. Used to be the same snowboarding until i got good boots and stopped tightening the laces up so much

And

medi-dyne.com/products/x-brace

Fixed my PF. Very painful could hardly walk. Still kited though ... Flat feet suck major cok.

bolt wakeboarding boots to your kiteboard.
Sh!t they're comfy you won't look back.

In the early days of kiting 2000-2004 I started to suffer plantar fasciitis. Back then the boards were very stiff and the deck pad were basically just gorilla grip.
Now the boards are softer and many of the deck pads are moulded to have quite pronounced arches.
I would recommend looking at other deck pads that may have a better arches to support the base of your foot.
Also try and set up the straps so they are tight on the sides of your foot and a little loser over the top, make them more U shaped. I achieve this by twisting the locking plate of the pad and strap so they run more along the lenght of the board rather than the width. I only do this to the locking plate on the inside of my foot.
As a last resort have some orthotics made for a pair of wakeboard boots and replace the straps with boots

Ive got flat feet and I have no problem when im using boots, i now only use straps in light wind.

I've got flat feet too, and I've found only two straps (so far) that I can ride in and they don't give me cramps and my feet don't slide out of them..
2014 Blank Force straps/bindings and the old Cabrinha custom lace up strap/bindings circa 2010.
I also find riding in thin surf booties helps.. The ones with either a split sole or reinforced neoprene sole, rather than rubber soled. I hate having to wear them but if it's a choice between flying out the board every time I leave the water or wearing the booties, it tends to win every time..
To be honest, like everyone else says, boots or Joints might be the easiest way to go!