DH, I store my hides dried flat on shelves in the closet until I tan them so not sure if I could store them any flatter.
For dryer breaking I take one dryer, lots of 2x4x4 inch pieces of wood and about 9 dried hides. I sponge my veg tan onto them until they are soggy but not dripping and let dry until just damp. Then I rub organic hand lotion well into them and let dry a bit more.
They are still damp and floppy when I toss them into the dryer to tumble on AIR DRY ONLY for about 6 hours.
Every time the air cycle times out I take the hides out and flatten them a bit as they tend to bunch up and crumple.
Not a problem, I just keep flattening them.
The fryer hides will come out totally finished and need no further breaking, Doe hides will need a bit more work and buck hides need quite a bit more but are worth it.
BUT all I have to do to finish the older hides is to dampen them with a bit more veg tan (Ultra strong brewed black tea) until they are totally flexible and rub with more hand lotion - not too much - and work by hand, wringing, twisting and gently pulling until totally dry. If they are drying stiff and I have time, I will dampen them a bit more and continue working but if I have run out of time, they just live half broke until I can get back to them.
The dryer breaking makes for easier hand finishing, at least for me. I have had a bit of tea staining on white hides but very little as I am careful when sponging it onto the hide side.
By using no chemicals on the fur side of my hides, when I am finished the fur is just like it was on the living rabbit, NOTHING has touched it other than gentle soap and water when first taken off the rabbit.
As I have said, doing it the above way makes for a flatter, but still rounded, hide but when I tan and break one totally by hand it is as rounded as when I was on the rabbit. Makes cutting squares a tad difficult.
However, I turned a fault into a feature when I turned the last one into a pillow. It worked a treat.