From 14 to 17 Is my guess, but I don't know exactly
Kadaj was never assigned an exact age by Tetsuya Nomura. However, it can be deduced (probably incorrectly). According to this Final Fantasy Wiki, Kadaj was "formed when Sephiroth's will refused to be absorbed into the Lifestream". If that is true, then since Sephiroth was 25 years old when he died (and would have been absorbed by the Lifestream) and since Sephiroth was 32 in Advent Children (when Kadaj first appeared), then Kadaj would be only 7 years old (32 - 25 = 7).