Store your Dockerfile in version control, either in its own repo with other Docker files or in the same repo as the app.

Use Jenkins (or preferred build system) to fetch the Dockerfile, your app, build the Docker container, and then docker push to your own private docker registry.

Bake your AMIs with your Docker image (tags are your friend). You don't want to have to scale and find out you're having problems fetching Docker images from your private registry. You'll still be using config management for the underlying Docker host.

Hope this helps!