A dwindling but still significant portion of my income comes from my darkroom work, and I ship handmade exhibition and museum prints all over the world, and I always ship them flat.
I put a layer of interweaving paper over the surface of each print, and then sandwich them between layers of thin acid-free mat board, then corrugated cardboard, foam core or gator board for stiffness. Sometimes I'll use two sheets of board over one side, and one sheet over the other side. The whole package gets taped together with acid-free artist's tape so the prints don't slide around. Larger prints and more expensive prints will get more expensive packing materials. On several occasions I've actually had to resort to making wood boxes to ship larger orders.
You have to remember that you are doing two things: protecting your clients investment and presenting your brand. Think about the beautiful and luxurious packaging of the best products, like Leica or Apple gear. I'm not saying you need to go to that extreme, necessarily; but you want to package to both protect your and your clients prints, and match the level of quality of the thing inside. I want my clients to be as impressed with the quality of the presentation and certain of the care that went into protecting their prints as they are with the quality of the prints themselves.