Answer
To store your Static Cling and prevent it from gathering dust and dirt, keep the original wax paper backing and simply re-apply the Static Cling to the backing when not in use. If you no longer have the original backing, ordinary wax paper from the baking aisle at the grocery store will work.
To prevent dust from settling on the cling, roll up the Static Cling and backing, graphics facing inward, and secure with a rubber band or masking tape.