The Admiral was/is the commander in chief of the Unlogic Project. Although direct battle field commands were/are given by "The Captain", The Admiral was/is always behind the scenes making sure they have what they need e.g. pebble transports.
The Admirals actual qualifications as a commanding rank officer in a galaxy wide star fleet are questionable. In a number of episodes his demeanor and abilities e.g. writing, are often bad to awful. This however makes him the ideal commander in chief for such a project as the Unlogic. His exact role, his mission brief and his authority are never in any episode explained or questioned.