Mesos

Use of private registries is supported. User needs to create a docker.tar.gz archive in his home directory containing .docker directory after successful login and mount his home directory in job.

Kubernetes

Not implemented. https://github.com/kubernetes/kubernetes/blob/1f952b05d3e56cf233c94f1b2c65f05e6cde5061/docs/images.md#using-a-private-registry

Swarm

Not implemented. https://docs.docker.com/engine/reference/api/docker_remote_api/

X-Registry-Auth header can be used for authentication but would need user to fill his credentials, or read .docker/config.json if it exists.