UPDATE: 29-07-2023 - use native method for Amazon Linux 2023 at https://docs.docker.com/engine/install/centos/
UPDATE (March 2020, thanks @ic): I don't know the exact AMI version but yum install docker
now works on the latest Amazon Linux 2. The instructions below may still be relevant depending on the vintage AMI you are using.
Amazon changed the install in Linux 2. One no-longer using 'yum' See: https://aws.amazon.com/amazon-linux-2/release-notes/