Born on May 13, 1841, in Chester, Chester County, South Carolina,[1] Brawley attended the common schools and graduated from South Carolina College (now the University of South Carolina) in 1860.[1] He enlisted as a private in Company F, Sixth Regiment, South Carolina Infantry, Confederate States Army on April 11, 1861.[2] He lost an arm in the Battle of Seven Pines and was retired from service.[2] He was manager of his family's plantation from 1862 to 1864.[1] He traveled and studied in Europe in 1864 and 1865.[2] He was admitted to the bar and entered private practice in Chester from 1866 to 1868.[1] He was solicitor for the Sixth Judicial Circuit of South Carolina from 1868 to 1874.[1] He resumed private practice in Charleston, South Carolina from 1874 to 1893.[1] He was a member of the South Carolina House of Representatives from 1882 to 1890.[1]
Following his retirement from the federal bench, Brawley lived in retirement in Charleston.[2] He died on November 15, 1916, in Charleston.[1] He was interred in Magnolia Cemetery in Charleston.[2]