That is indeed the 29th Tennessee's Second National made by Mrs. Charles Platt of Augusta, GA. Charles and his brother Jacob were prominent local flag makers in Augusta, Jacob probably making the 1864 AOT battle flags for the Augusta Depot.
When regiments formed, assuming that all ten companies got flags presented to them, one was usually chosen as the regimental flag. Sometimes units also got specific regimental flags in lieu of choosing a company flag.
Greg Biggs