It doesn't make sense at all.
To be honest, the Defiant being Siskos personal starship doesn't make THAT much sense either, even though it's home base is DS9, it really ought to have it's own C/O.
Kira commanding it makes no sense whatsoever, it's a starfleet vessel and she's not starfleet. It's that simple.
US Navy and British Navy might share a port for instance and have an agreement between command officers but a British commander isn't getting on a US Navy ship and taking it out on a mission or vice-versa