It was clear that Kirk regretted his promotion, so I have a hard time seeing him doing it twice.
But how much say would Kirk have in the end? He's an employee, a resource for Starfleet to utilize. He may simply be told "we want Admiral Kirk, and have no use for Captain Kirk - wanna this fancy star or these discharge papers?", and that's that. Starfleet did seem to keep him in a display case of sorts, using him as a prolific and profilic instructor (Academy Commandant?) and never sending him anywhere; clearly, he wasn't being asked what he wanted to do.