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from storage - if you don't explicitly attach it, Prefect uses local storage and attaches the hostname as a label so that related flow runs will only be picked up by agents that can access this local file

Yes prefect will push the Flow to S3 for you and that shouldn’t have the default label. If you use local storage with ECSRun to point to the file inside the container, you can do:

storage = Local(.., stored_as_script=True, add_default_labels=False)

or you can do:

flow.storage.add_default_labels=False

Not sure whether relying on env variables for that is a good approach. You mentioned you need some pointers - this Discourse topic is dedicated to this problem in its entirety. specifically, this code snippet may help build such logic via a simple function