He is Kenshin and Kaoru's son who appears at the end of volume 28. He likes to climb things but cries whenever he can't get down. He loves his mother but doesn't like his father. (He likes to pull Kenshin's hair)
In Samurai X: Reflections, he is still a toddler, but some scenes skip to the when he is fifteen years old and trains with Hiko. In the OVA time line, Kenji grows up without Kenshin's presence. He watches as his mother mourns his father's continued absence. Kenji grows to resent his father's selfishness and his mother's continued depressions.
At age 15, he runs away to Kyoto to train under Hiko Seijuro XIII in the art of Hiten Mitsurugi Ryu. Kenji displays a lot of promise as a student, just as his father had 30 years before, but Hiko decides to honor Kenshin by not passing the school on to Kenji. Hiko basically keeps Kenji busy until Myoujin Yahiko shows up to take him home.
Kenji refuses to leave, saying that he wants to experience true strength and surpass his father's legend. Yahiko and Kenji duel. Kenji shows his promise and his genius, but Yahiko uses his beliefs and experience to conquer the teen. After Kenji is subdued, Yahiko passes on the Sakabatou to him. Kenji then returns to Tokyo with Yahiko to be with his dying mother.
At the end of the OVA, we see Kenji with a girl named Raikoji Chizuru. Kenji now wields the Sakabatou and seems to be at peace with his father.