Vinyl floorings are made to resemble other types of flooring, including wood and tile. Everyday use of the floors and walking on the floors creates scuff marks and other scratches. It's impossible to remove those scratches, but it is possible to hide the scratches.
Pour lighter fluid onto a soft cloth and gently rub across the scratch until it disappears. Wash the vinyl flooring with a vinyl cleanser. Use a vinyl floor finish to protect the area against future scratches.
A small amount of baby oil or spray lubricant works if you can't find lighter fluid or you're worried about using it on the floors. Apply the liquid directly to the scratches and gently rub into place with a dry cloth. You may need multiple coats to completely hide the scratches.
If using lighter fluid, gently wipe the area with a dry cloth to remove as much of the lighter fluid as possible. Remember that lighter fluid is a flammable material.