I use various boxes & bags to both store & carry flies. I have 2 of the boxes that Dennis posted. They're my boat boxes. I use different size Plano/Flambeau boxes to keep my extra flies, several fly boxes for different types of flies that I'll carry, and a couple of the bags that are normally used for plastic baits. I use them for some bigger flies, and add some extra inserts so I have quite a few flies in a bag.
I don't have pictures of the bags, but do have some of the various boxes I use.
This is a Fox Box.
My 2 boat boxes. Same as the box Dennis posted.
Waterproof Fly Boxes.
Medium Plano/Flambeau box.
Another Medium Plano/Flambeau box.
Flambeau box, polystyrene. Clear. I used these for display when I tied flies commercially. Don't like carrying them as this type plastic cracks easily, but they're great for storage.
Smaller Plano/Flambeau box.
Small Pocket Size Flambeau box. This one is several years old.