Phillips obtained his bachelor's degree in Biochemistry and Chemistry from Rice University in 1974 and followed it with a Ph.D. in biochemistry from the same institution in 1976. He also held a Robert A. Welch Predoctoral Fellowship from 1974 to 1976 and received a Postdoctoral Fellowship from the National Institutes of Health in 1977 as well as a Research Fellowship from the Medical Foundation in 1980.