If you have a shelf big enough, just put the board on it. If you must place it in a closet stand it straight up & down as possible. Veneer boards hold up good in storage. I am not sure about solid wood boards.
Storing chess boards

As a solid wood chess board manufacturer, I believe it is best to store a board on a flat surface. If you have multiple boards you can put a soft cotton cloth, like an old tee shirt, between the boards. Never cover or wrap the board in plastic, the wood has to breath. The climate is more important than anything. Never store a board where it will see natural sunlight. Also never store it anywhere damp or hot, like a basement or an attic. If possible, it should be kept between 40-60% humidity and 60-90 degrees F.
This may be a dumb question, but what is the best way to store a or multiple chessboard(s)?
Is there a difference between veneered and solid boards? (eg front & back of the board getting equal exposure to air moisture etc)
tnx in advance!