If you want to use a Jenkins JNLP slave (like he amazon-ecs plugin relies upon) with a Jenkins master that uses a self-signed SSL certificate, then you may wish to build yourself a new Docker image that pre-bakes that certificate into the Java CA trust keystore. See JenkinsJNLPSelfSignedCertificates for more information.
The amazon-ecr-credential-helper tool helps makes it a little more convenient to push your Docker image back up to Amazons ECR.