no age specifically but either Duke or Batman (I forget which) indicate he has trained with Bruce for approx. one year between leaving the We are Robin movement (where he was stated as being 16) and starting his superhero career as The Signal in Batman & The Signal. so the most concrete age we have for Duke (if you follow Duke's story) is about 17.
Year of the Villain kinda mucks things up a little since we know that runs concurrently with his time on the Outsiders. the event is supposed to take place over the course of one year, meaning he should technically be 18. however l, since YoTV leads into Death Metal, which messed with space and time, it's pretty safe to assume DC will skirt around the time elapsed on that. so it would be simpler to just think of him as vaguely senior in high school age (16-18).