Henry completed preparatory studies and then studied law. He was admitted to the bar in 1803 and commenced practice in Chillicothe, Ohio. For a time, he was in partnership with his brother, Platt Brush.
After completing preparatory studies, Henry pursued legal education. In 1803, he was licensed to practice law in Chillicothe, Ohio. At one point, he shared a practice with his brother, Platt Brush.