If you can get a matching piece of linoleum just a tad bigger than the burn mark itself, you can make a decent repair.
Place the new piece over the burn mark and cut through the piece and the burned piece at the same time. This will give a perfect fit for the new piece. Clean out the removed burn spot and glue down the patch. If you do this carefully enough and have matched the color and or pattern it will become invisible or at the very least less noticable than the burn mark.