Deep Space Nine wasn't actually a Federation Starbase during the series. It was a Bajoran Station under Federation Administration. Given that, it stands to reason that command of the Defiant would have been granted to Kira as a courtesy/part of the treaty just as command of the station would have been granted to The Federation. I'm sure if Bajor had really pushed the issue, a Bajoran officer could have been in command from day one.
I imagine Kira would have command authority on all Federation assets within the Bajoran Sector as part of the agreement between Bajor and the Federation. However if Kira were to go aboard the Enterprise in a different sector for example i'd imagine she would be an observer/consultant and only be given command authority if Picard authorised it.
I did notice though that once Worf arrived on the scene Kira commanded the Defiant a lot less.