This is all I could come across. No military records!

Dr. George Newton Flowers Believe a Physician

“A pioneer citizen of Doraville and long time postmaster of the community."

Atlanta and Environs: A Chronicle of Its People and Events, 1880s-1930s
By Franklin M. Garrett
page 724

https://books.google.com/books?id=7qpif6-Z5o4C&pg=PA724&lpg=PA724&dq=Confederate+Soldier+George+Newton+Flowers&source=bl&ots=nvVGO7iSJO&sig=ACfU3U2bfYDCVjmpJx-Yh1iYzT1lz3ctdg&hl=en&sa=X&ved=2ahUKEwiH1M3m-fzmAhVUYs0KHZnGBfYQ6AEwCnoECAoQAQ#v=onepage&q=Confederate%20Soldier%20George%20Newton%20Flowers&f=false