"By Sosuke Aizen having been a Captain of the Gotei 13, he has achieved a Bankai..."
Never proven. Kubo might be thinking he has one, but until he comes out and says it, it's a believable assumption that Aizen used his Kyōka Suigetsu's Shikai to mimic the appearance of a Bankai during his exam.
And, let's face it: with a Shikai that powerful, who the hell would want to take it up another step? What could possibly be better, as a Bankai, when the Shikai can do such a thing? Control time and space? We've already seen that as a Shikai in the filler "Gotei 13 Invading Army" arc, and it's already been covered that no two zanpakuto are alike. And yes, I know it's filler but Kubo wouldn't have approved of that Shikai ability in the arc if he'd intended it as a possible Bankai for Aizen.
It'd be believable that his Bankai, assuming he has one, would be substantially weaker, or less effective, than his Shikai. Like, in my opinion, Soi Fon's Bankai. YAY IT'S A MISSILE. Who cares? It couldn't kill Baragan. But Suzumebachi (which has the nickname of 2 hit certain kill or something like that) might possibly have done the job. Again, that's just how I view her Shikai/Bankai. It's conceivable that Baragan might have been even less affected by the Shikai than he was by the Bankai.
In closing, I'd like to state that who cares anymore. Even if he escaped from the prison he's been shoved in by the Soul Society at some point, the question of his Bankai becomes a moot point since, approaching his defeat, the Hōgyoku had determined that Aizen "no longer needs a zanpakuto", therefore either severing his spirit's ties with Kyōka Suigetsu entirely, or just destroying the sword. In either case, Aizen no longer has a zanpakuto with which to release a Bankai.