The Display Cover feature is only supported on some Kindle devices without ads. These devices include the Kindle (8th, 10th generation), Kindle Paperwhite (7th, 10th gen), Kindle Oasis (8th, 9th, 10th gen), and Kindle Voyage (7th gen). If you can’t recall which Kindle you have then click here to identify it. Promotions on ad-supported devices can be disabled for $20, or by calling into customer support and asking real nicely, according to many reports on redditkindle.
Supported Kindle devices running the latest firmware can activate the Display Cover feature by enabling the Show Cover option under Settings, Device Options