We could settle this with stardates. (Or then with baseball bats at dawn, whichever is less painful.)
Memory Alpha lists quite a few stardates for the final episodes, yet none of them actually feature stardates in dialogue. The numbers are derived from various computer graphics and the like. If we trust those graphics, the final two episodes take place around SD 52800, whereas the early ones tend to have dates in the SD 52600 ballpark. Yet 200 SD units amounts to a whopping one-fifth of a year in DS9 style of reckoning! (And that's pretty consistent elsewhere in DS9, plus in TNG and VOY and retroactively even in TOS...)
Could Kira have been hiding there for more than two months? Why not; it's not as if there'd be any hurry. Except of course Odo slowly succumbing to the disease - but that's handled within the scope of the "52600 episodes" already. Basically, two months might have passed between "Extreme Measures" and "Dogs of War", in which time Odo fully recovered, Sisko got his new ship, and the Dominion finally located Damar's resistance movement's "secret underground headquarters"...
In absence of contrary arguments, I'd thus indeed claim that the interval was two to three months. Although Damar might have retreated to Mila's basement towards the end of those months, not right from the start; Mila doesn't make it sound as if the rebels have been spending all their time there for the past few months, until recently.
Timo Saloniemi