Kinzou looks up to Kinji as a younger brother. He envies what Kinji has and tries to obtain it for his own. He always wanted to live the peaceful "boring" life that Kinji has. We find out later that Kinzou is actually a genetic son of Konzou Tohyama. Kinji often calls Kinzou a "tsundere" due to his prideful nature on the outside but caring and vulnerable on the inside.
It's not really known how much Kinzou and Kinichi interact with one another, but we do know that Kinzou went out of his way in volume 11 to bring Kinichi to the oil plant so all of them could meet.
Kaname and Kinzou are siblings, and although he doesn't show it very often, he does care about Kaname's well being and tried to not lead her more down the path of destruction then he already has. As shown when he broke ties with her in the GIII League arc and started calling her "Kaname" instead of "Forth".
Kinzou wanted to use Aria's power to go back in time to save professor Sarah.