There are really two kinds of outdoor kitchens, and they move completely differently. A modular stainless cabinet system unbolts and rolls away like large appliances, while a built-in stone kitchen with a plumbed gas line needs professionals before you touch a wrench.
Pro tip: Photograph every module's position and cabinet-to-cabinet connection points before disassembly so reassembly at the new address is a puzzle you have already solved once.
Watch out: Never disconnect a hard-plumbed natural gas or propane line yourself; an improperly capped line is a fire and explosion hazard and typically requires a licensed plumber by law.