The 1st Tennessee's Augusta Depot flag is based on the period drawing of it at Kennesaw Mountain. We can only assume that the artist was accurate.
As for the 20th Tennessee, since this flag does not survive we cannot tell for sure what it looked like.
The 2 inch white fimbration was where the battle honors were typically added for these flags. The red field is where the unit designations were usually placed with the digits in the upper quadrant and the state in the lower. Virtually all of the AD flags I have seen that do have unit markings are done this was (with a couple exceptions).
The 20th TN was in Bate's Division in May, 1864 for the Atlanta Campaign, more specifically in Smith's Brigade. The only flag from this brigade that survives is the flag of the 4th Georgia Sharpshooters which is a 12 star variant of this pattern issued to them in 1863. But flags still survive in Lewis' KY Orphan Brigade and Finley's FL Brigade and those are indeed marked as I described pretty much. This division served in Hardee's Corps. Hood's Corps did issue orders in March, 1864 to have their flags properly marked. Hardee's Corps followed in April, 1864 with similar orders.
Some of my favorite battle honors for this pattern can only be found on the flags of Brown's TN Brigade. Since this brigade, along with Cumming's GA Brigade and Pat CLeburne's Division, held their line and even cleared their front of Federals at Missionary Ridge in late November, 1863, they had their flags decorated with this honor - "Missionary Ridge (Right Wing)"
This was a big slap in the face of the rest of the AOT that fled from the ridge in that fight.