马 depicts a horse's mane and four legs. As radical it marks 驯 as something done with horses - the prototypical animal humans broke and trained. Joins 骑驾驰 in the equestrian family.
川 supplies the sound (chuān drifted to xùn). Three flowing parallel lines - water finding its course. The combined image is fitting: a horse made to flow like a river, gentled into yielding obedience.
