Brinkley began his career by serving as a law clerk to Chief Judge Sam J. Ervin, III of the United States Court of Appeals for the Fourth Circuit.
He then entered the practice of law in Raleigh, North Carolina, first with Moore & Van Allen, PLLC, where he became a partner in 1998, and from 2003 to 2015, with Smith, Anderson, Blount, Dorsett, Mitchell & Jernigan, LLP.
[4] Brinkley is the first person since the nineteenth century to become dean of the UNC School of Law (founded 1845) directly from private practice.
For seventeen years (2004–21) he was Vice Chancellor of the Episcopal Diocese of North Carolina, and succeeded Edward L. Embree III as Chancellor of the Diocese in November 2021, becoming the principal legal adviser to the Right Reverend Samuel Sewall Rodman III, XII Bishop of North Carolina, and various diocesan institutions.
[4] He is an elected member of the American Law Institute and an honorary Master of the Bench of the Honourable Society of the Middle Temple.