He is second to the Minister of War who answers directly to the Dark Council, so that does give Kilran some authority. This technically makes him the number 3 in command of Imperial Forces, though I do not think it is specified which Sphere of Influence the Minister of War and Kilran are serving under, Defense of the Empire (Darth Marr), Military Offense (Darth Vengean/Baras) or Military Strategy (Darth Decimus).
Well I see it a bit differently. I see Grand Moff being equivalent to Commander-in-Chief which is usually held by the president of the country and minister of war being subservient. This is further reinforced by the number ministries you mentioned. It would make sense that Grand Moff is being above all those ministries.
If you don't mind me asking. You wrote that Grand Moff is number 3. Was that described by some canon Star Wars source or did you just make the logical assumption?