As for Kirk's rank? That's a big fat Meh, as far as I'm concerned. If you're going by his Admiral uniform in TWOK? Don't. I doubt there was ever a pattern to the Monster Maroon Admiral unis - rank insignia, those little yellow stripes on the inside of the jacket flaps, etc. were all basically thrown together at random.
I mean, it's not like you could look at various Admirals such as Kirk, Morrow, Cartwright, Bob from ST V, Bill from ST VI, etc. and work out their precise order of seniority just by their uniforms...it's all a crap shoot, really.