CoolSculpting is a great treatment because it kills fat cells permanently. Results are essentially permanent as long as you maintain your overall weight. You will of course continue to age as normal and might find that eventually the skin under the chin will become more lax - as it would regardless of whether or not you had CoolSculpting - but the pocket of fat in the double chin would essentially be reduced for good.
Much like CoolSculpting done on other areas of the body, results to the double chin can be permanent as long as you maintain a healthy diet and an active lifestyle and don't gain too much weight. Most people need 2-3 treatments to the double chin for the best results. Best wishes.