we know she confirmed the autodestruct alongside Sisko, which  pretty much cements her role as directly below Sisko prior to Worf's  arrival
		
		
	 
She even identifies herself as First Officer, and people demanding this  sort of access from a starship computer tend to give their identities  with respect to the ship's hierarchy (say, our heroes in ST3:TSfS  probably aren't even officially 
Enterprise officers any more, yet  Chekov's bid for self-destruct authority is "Acting Science Officer", a  title he apparently invented for himself on the spot).
I guess any qualified officer may contribute to a self-destruct order;  it doesn't need to be done in a strict order of hierarchy. In all  likelihood, it's just set up like a game of poker: if any three officers  give the order, it can only be countermanded by the same three, or by another trio whose ranks and positions comprise a "higher hand". That way, Ensigns Huey, Dewey and Louie can't blow  up the ship from underneath Picard - and, more relevantly, they can't  stop a heroic self-sacrifice ordered by Picard, such as in "Where  Silence Has Lease". 
This in mind, Kira in "The Adversary" 
could in theory have been  subordinate to the highest-ranking Starfleet officer present - to wit,  Dax. But the mission involved a conflict with the Tzenkethi, supposedly  neighbors of Bajor since the DS9 team was tasked with this in the first  place, and Sisko would probably have wanted to maintain Kira's public  status as a prime doer and decider on such a politically important  mission, not take it away from her even if Starfleet regulations  allowed.
...Enough second-guessing; the above lists look okay to me. Although there are probably a dozen officers between Dax and O'Brien, considering we saw plenty of 'em aboard, and considering we never saw O'Brien take command even when numerous main heroes were absent.
As for Dax' high standing, let's remember that the station didn't have  too many officers to begin with. In "Emissary", Dax might be one out of  just a dozen, and one of only two Lieutenants. Even after Starfleet  replaced Lieutenant Primmin with Lieutenant Commander Eddington, there  was a distinct shortage of high-ranking officers on the background, so  letting Dax command the 
Defiant every now and then sounds  sensible to me. She'd certainly have fewer stationside commitments than  Security Chief Eddington (and never mind that Eddington never appeared  to get a high-ranking successor after his defection).
Timo Saloniemi