I've had it happen. No luck washing it out. Enjoy your new patterns.
You just have to lay or hang the kites out to dry after sessions when you get home. I've had this happen with salt water also. Less, but it still happens. I think in the salt waters case, the dampness can still cause condensation which then causes mildew if you leave it rolled up in the right temps/conditions.
I have had luck (when I'm unable to hang them) to fold them very loosely, unbagged, so they can breathe and dry slowly. That's only for slightly damp kites, though... not if it went for a swim.