How can I insulate the plywood before replacing the vinyl flooring?
You would insulate UNDER the floor, not between the floor plywood and vinyl. To properly insulate your kitchen: normal insulation material (fully enclosed is preferred) is applied between the Floor Joists. To access this area you need to get into the "crawl space" under the floor you want to insulate. NOTE: All floors (for main floor level rooms of a house) should be accessible via the crawl space, and all rooms should be insulated (for best heat retention). Special hangers are made for installing under-floor insulation, or: 1. chicken wire 2. strips of wood can be cheaper method of "hanging" the insulation between the floor joists. NOTE: Insulating water/sewer/electrical wiring under floor(s) can lead to problems locating them later. Plan ahead... for future access to these.