Gendry is the last living member of Robert's immediate family. Unbeknownst to Robert, he produced no true heirs with Cersei, but since Ned's attempt to expose the incestuous parentage of Joffrey, Myrcella, and Tommen failed, in the eyes of the Seven Kingdoms, they were next in the line of succession after Robert's death. With all three of Cersei's children dead, having produced no heirs, Gendry's claim could be strong if he had anyone with clout championing him.
With both of his uncles and his cousin Shireen dead, Gendry is the last of the Baratheon line. However, he's also a bastard. That means he would have to be legitimized in order to claim the throne, and he doesn't seem to be interested in ruling. Much like his father, Gendry appears to be more of a fighter than a king, and even if he was legitimized, he probably wouldn't pursue the Iron Throne.
