Well, since Pokémon Leagues are yearly events, and he participated in the Indigo League when he was 10, that means he must've been at least 11 when he participated in the Silver Conference, and then 12 when he was in the Hoenn League, and who knows how long it took he and Haruka to get to and participate in the Grand Festival. All of that aside, he's at least 14 and, at the most, 15.