Breckinridge hailed from the Breckinridge family. His grandfather was major general Joseph Cabell Breckinridge Sr. and among his uncles were Joseph Cabell Breckinridge Jr., an officer in the United States Navy during the Spanish–American War, and Henry Skillman Breckinridge, who served as the United States Assistant Secretary of War under President Woodrow Wilson. He was the great-great-grandson of John Breckinridge, who had served as the second Attorney General of Kentucky and in the Kentucky House of Representatives and who also served as a member of the United States Senate and as Attorney General of the United States. John B. Breckinridge was also the great-nephew of William Campbell Preston Breckinridge who also represented Kentucky in the United States House of Representatives.