Well, "open source Heroku" implies that they're compatible with Heroku's API. That means application release management, runtime configuration (config:set), application collaboration via "sharing"... From what I see in https://github.com/flynn/flynn/tree/master/demo, half of the API isn't there yet. We'll see how it goes over the next few months.
We certainly not cloning Heroku's API, but we have most of the things you describe and much more in our API and CLI, including release management, configuration, job control, resource provisioning, log access, docker image releases, interactive and detached one-off processes, etc.
