What is the right order of work in a kitchen remodel?

Design and cabinet order first, because the lead time on cabinets sets the whole schedule. Then demolition, then any framing, then rough plumbing and electrical while the walls are open, then inspection, then drywall and paint, then flooring, then cabinets, then countertop templating, then the countertop, then the backsplash, then plumbing and electrical trim, then appliances. Flooring before cabinets is deliberate: it lets an appliance be replaced later without a lip at the edge of the opening.