Spread the tablecloth, vinyl side up, on the lawn on a hot day in direct sunlight. If you don't have the yard space, lay it out on the hood of your car. By the end of the day, your tablecloth should be free of wrinkles.
Iron the tablecloth vinyl side down on the lowest setting. Put a cloth between the iron and flannel side of the tablecloth, and carefully apply pressure as you iron.
Put the tablecloth in the dryer on the lowest setting with a few damp towels. Check it often to make sure it isn't getting too hot. Take it out while it's still warm, and smooth out the creases.