Tablecloths that have a flannel backing usually have a plastic or vinyl face. Inexpensive and long lasting, vinyl tablecloths wash nicely, but drying leaves wrinkles on its backside. These wrinkles also show up on the front side of the tablecloth, resulting in bumps and creases when on the tabletop. While you can't iron the vinyl directly, try any one of these solutions to get the creases out of your tablecloth.
Iron the flannel side of the tablecloth. Place the iron on a low heat setting and let it heat up. Set the tablecloth on the ironing board, plastic side down, flannel side up. Starting at one end of the tablecloth, iron out the wrinkles, without the iron resting on the flannel for too long in any one spot. Always iron on the flannel side of the tablecloth to avoid the vinyl sticking to the iron. Use the steam function periodically to speed the process along.
Steam the vinyl tablecloth on the flannel side using a portable garment steamer. Garment steamers work well for getting the wrinkles out of clothing or materials that cannot be dried in a hot dryer. Hold the steamer about 3 to 6 inches away from the flannel backing. Periodically check the front side of the tablecloth to ensure wrinkles are gone.
Hang the vinyl tablecloth outdoors on a clothesline in the sun. The sun often heats the vinyl enough to remove the wrinkles from the flannel.
Throw the tablecloth into the dryer for about five minutes with a small wet towel. This will prevent the vinyl from heating up too much. Remove the tablecloth and check it for wrinkles, if still wrinkled, set it back in the dryer for a few more minutes, standing by to ensure it doesn't overheat. Remove and lay flat as it cools.