So many people are incorrect here.... On a few things.
1: Yes. Kisame's goal that he was willing to give his life for was the Eye of the Moon plan. If he and Itachi came to a point, such as whether to capture a jin or not... Kisame would act on Itachi.
2: Kisame might of known, there's strong enough evidence to support the idea that Kisame knew Obito was not actually Madara.
3: Kisame would first check in with Obito, unless it was a heat in the moment thing. If Obito deemed that Itachi was still useful, Kisame would play along.
4: Kisame and Itachi are close enough equals in power to the point where it would be bad for either one to fight each other. To say Kisame would be stomped or was too afraid is foolish. Kisame didn't show fear to battling a perfect Jin. Itachi he would take on, somewhat sadly, but with a steel resolve nonetheless.
!? Anyways if he did he would have a good reason why to not try to kill him, but I think he respected him, because he was the only member of the Akatsuki who wasn't as deranged as say Hidan. He added more flavor to the group which is why he liked having Tobi in the group.
