Board Thread:Questions and Answers/@comment-9826910-20130618064245/@comment-11051098-20130625212546

Only recently learning his Zanpakutô's name, I doubt Kenpachi will learn Bankai any time soon. Byakuya once said it takes 10 years normally to achieve Bankai, and many more years to master it.

So unless he gets help from Yoruichi with the device Urahara invented and succeeds achieving Bankai in 3 days, I don't think he will achieve it during the story. But knowing his Zanpakutô's name, he could learn some techniques and/or attacks. Or just get more powerful, as he will likely fight alongside his Zanpakutô now.