Companies F & H were raised in Green County.
Appearing in the Friday, August 16, 1861 issue of the Athens (Tenn.) Post is a description of the presentation of a banner to Captain McClelland's Company A by the ladies of Charleston, Bradley County, n.d. Unfortunately, there is no description of the flag other than a mention of stars, blue field and bars which would signify it being of the First National Pattern, Stars and Bars.
I did a Goggle search of the 29th and came up with this description and picture of a later Stainless Banner, non-combat, presented by the ladies of Savannah, see:
http://home.comcast.net/~the29thtn/historic29th.htm
2nd National, Stainless Banner
Greg, is this the flag you referred to? As most companies were presented flags on departure from their home ports, how were regimental colors developed?
George Martin