Is it possible to reuse my MacBook cover on another device?

Glitty wood covers for MacBook and iPad are not intended to be detached and reused on other devices. Most likely the wood will break as you take off your MacBook.
Although intended for one time use, Glitty leather and Glitty stone covers are more flexible than wood. If you are careful you should be able to remove the cover in one piece. Be careful not to stretch the skin as you remove it so that it retains in shape. The cover should stay sticky enough that you will be able to restick it to another MacBook.