The ps command can be used to determine if your system is using init or systemd. If PID 1 is init, then you will use the service command. If PID 1 is systemd, then you will use the systemctl command.
If your system is using systemd, use the systemctl command to start and enable docker.
systemctl enable docker systemctl start docker systemctl status docker
chkconfig docker on service docker start service docker status