I like to keep 1/4, 3/8, 1/2, and 3/4 inch Baltic Birch in the shop just to have on hand when needed. In my experience, Baltic Birch tends to stay flatter than other plywoods, but it can bend and warp, too. When I go to the store, I avoid the pieces that are already warped. The thicker pieces tend to warp less.
I recently took out a piece of 1/4 inch Baltic Birch that warped while stored in my shop. I improved it by setting the edges on some books on a large table, piling more books on top down the middle, then leaving it set for several days, checking it once in a while to make sure it didn't warp the other way. After 4 or 5 days, it wasn't perfectly flat, but it was much improved and useable. That trick may not work with 1/2 inch and above.
It would be nice, but I don't have space to store them flat. One of these days, I want to build racks and carts, so they don't rest directly on the concrete floor, which I know is not good for any stored wood.