He (along with Sideways Sawyer) is one of the big question marks in the sideways timeline, isn't he? We know he's there, but he was probably one of the characters most heavily manipulated by island connections in the original timeline -- connections that are either absent or at least very different in the new timeline. Therefore, it's anyone's guess what he might be up to at this point. I'm sure we'll find out soon. Whatever it is and whatever he has been doing, I expect that he is or will be heavily involved with Sideways Charlie, mirroring the connection between the two on the island in the original timeline.
I have a theory about Sideways Jack's mysterious minor wound on the plane (when he examined himself in the plane's lavatory). I think that was a symbolic clue that the original timeline is literally bleeding through to the new one. Other clues to this are his puzzled looks at Desmond and Kate, indicating an almost-remembered familiarity with them. Of course, he directly questions Desmond about this out of a fuzzy sense of deja vu. He might have remembered his touristad encounter with Desmond from years earlier -- but I have serious doubts as to whether that encounter would have happened at all in the new timeline.