Kenny started his rugby career at Marr College before joining Marr RFC and then moving to Kilmarnock in 1995. In 1999 he switched to Glasgow Hawks. He was a mainstay of the club during his three seasons with Hawks, playing in two cup finals at Murrayfield.
Kenny has represented Glasgow District at senior level and was called in as cover for the Glasgow Caledonians (now Glasgow Rugby) late in 2000-2001, making his debut at Swansea in the final match of that season. Again drafted in, he appeared in the professional team's last four matches last season, scoring four tries. He joined Glasgow Rugby last season.