When Byakuya said "...my senior" he is referring to Ukitake, of whom is one of the first students of Yamaji. Therefore, Ukitake is older in age and place than Byakuya, hence the "...my senior". Budweineken is correct. Just a simple manipulation of the english language.

"Think again. When Rukia became part of the 13th squad, Bayakuya was already a Captain. How can Kaien then be his superior when Kaien himself is only a VC?" - EpyonNext

My explanation explained your statement.

And like I've stated, Rukia said it herself that Byakuya was only appointed the rank of Captain SHORTLY BEFORE Rukia has been admitted to the Kuchiki Family. Therefore the theory that Isshin is the previous 6th squad Captain is arguable and feasible.

Good Idea Budwineken. I place my bet that Isshin is the former captain of the 3rd.