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