It sounds as if you don't have read access to the document.
Are you generating a new instance of the class System.FileDocument? I would always recommend making a subclass and giving the user access to that entity specifically.
Even though the microflow might execute a download action, when the browser interprets the response, the identifier that it should download doesn't seem to exist (the server won't return the details if the user doesn't have access). Because of this it's likely that you will never see any feedback from the server.