Since it's already sliced to laminate thickness, we'd probably store this between two thicker boards, secured with some c-clamps.
The main thing you want to do is keep it from changing moisture too rapidly so you don't get cracking or checking, so keeping it in the house with temperatures and humidities that suit you are probably fine. Keep it away from heating vents or in the direct path of your a/c vents.
The weight or pressure from the clamps will keep it from potato-chipping out, and that is a technical term.
It's a lovely board, reminds a bit of
Ghost Crow, which started out as
this board.