Lacking time to research this further, I'll go with what I have found so far. I could not locate any source that mentions a percentage of Georgia's historical record going up in flames when Sherman burned Atlanta on November 12, 1864. An estimated 40% of Atlanta went up in flames, primarily in the business district. But that fact alone wouldn't give a percentage of Georgia's historical records destroyed.
Georgia's historical records would reside at the State Capitol and Archives; during the Civil War, the Georgia State Capitol was in Milledgeville, Georgia, some 100 miles southeast of Atlanta. Milledgeville fell to Sherman on November 22-25; some burning occurred here (primarily parts of the business district, the State Penitentiary , and State Arsenal). Although the State Capitol was vandalized, neither it or the Governor's Mansion were burned. Papers were scattered around in the State Capitol, but little else. All in all, Milledgeville got off light.
A visit to the Georgia Archives website sites that they have records going back to 1733, so that indicates most (if not all) of Georgia's
historical records survived the war.
So, my take is that few (if any) of Georgia's historical records were in Atlanta at the time of the burning on November 12, 1864. If any were, their number would not add up to a percentage point. My answer to the question is: None; 0%.