Yep - that's one of the Brown's Brigade flags that have the "Missionary Ridge (Right Wing" honors - although not much is left of the honor as you can see (we have this flag at the state museum and it has been conserved - you can still see part of the "right wing" honor).
I would try and math the AOT flag of the 6th Kentucky since they were of the same division as the 20th TN. The honors would be similar as they and the Orphans were in some battles outside of the AOT earlier in the war.
I would guess that honors for: Shiloh, Vicksburg (1862 - not dated), Baton Rouge, Murfreesboro and Chickamauga would work - as the 6th KY flag bears. The KY flag has crossed cannons inverted so you will have to find out of the 20th TN ever captured colors to earn that honor.
Geoff Walden has an excellent website for the KY Orphan Brigade - if you Google this it will come up and you can see a picture of this flag - which is also depicted in the Time-Life "Arms & Equipment of the Confederacy" book.