Steps how to install Docker and Docker Compose on Amazon Linux 2.

Install Docker

$ sudo amazon-linux-extras install docker
$ sudo service docker start
$ sudo usermod -a -G docker ec2-user

Start at boot.

$ sudo chkconfig docker on

Install git (optional).

$ sudo yum install -y git

Install Docker Compose

$ sudo curl -L https://github.com/docker/compose/releases/latest/download/docker-compose-$(uname -s)-$(uname -m) \
-o /usr/bin/docker-compose
$ sudo chmod +x /usr/local/bin/docker-compose

Check

docker --version
docker-compose --version