Resilient flooring or linoleum is one of those finishes that must not only look good but is subjected to a tremendous amount of wear and tear. For this reason, this is one of those instances where we recommend you consider leaving this one to the professionals. A professional repair could save you from having to replace the entire floor.
The repair technique employed by the repair contractor will depend upon several factors, such as, the age of the product, the quality of goods (cushion or inlaid), and the location of the burn. If you have a scrap of the original flooring, or if the pattern is still in production, then the best fix would be a small patch. Even if you don't have any scraps, or if the pattern has been discontinued, chances are that a small piece can be removed from underneath an appliance like the refrigerator.
The person making the repair will remove the small damaged section and replace it with the repair piece. He or she will make sure to pay attention to pattern-match and will take the time to make clean and well-sealed seams. Chances are that only you will know where the patch is located.