According to SFGate, to clean yellowed kitchen linoleum, apply a bleach solution followed by a vinegar solution and take care of any remaining trouble spots with a paste of water and bleach scouring powder. To clean yellowed linoleum, rubber gloves, a bucket, a measuring cup, bleach, lint-free cloths, a lint-free mop, white vinegar, bleach scoring powder and a scoring pad are all necessary items to have.
SFGate states that the bleach solution should contain 1 quart of bleach and 1 gallon of cool water, soaked into a lint-free cloth. It is important for the water to be cool or cold, as using hot water can damage the linoleum. Wash over the floor with the cloth, keeping it saturated, and allow the bleach to sit between 30 minutes to an hour.
Soak up the solution with a dry, lint-free cloth or mop, then rinse the floor with cold water. Clean out the bucket, then fill it with 1 gallon of equal parts vinegar and water. Soak a mop with the solution and go over the floor again. Rinse the floor once more with cold water. Finally, use the bleach scouring paste with a scouring pad to clean any remaining yellow areas. Repeat as needed.