The book "Volunteer Banners: Tennessee's Civil War Flags" will be published by UT Press and is projected for late 2009/early 2010. Thanks for the interest.
The flags used by Bate's Division would have been the rectangular flags made by the Augusta Depot. You can see examples of these flags on our Flags of the Confederacy website - www.confederateflags.org I will have to check and see if these might have been marked with a unit designation or not - some were and some were not. Typically, if marked it would have the number in the upper quadrant and the state in the lower - for example "26th" for the upper and "Tenn" for the lower (as this flag is actually marked). These would be cut and sewn white cotton letters.
Tom Martin is on this board a lot and he can help you with quotes for proper Augusta Depot flags.
As for the Minnesota troops I would check with their state archives and see if they have pictures of them that you can purchase. These would be the 6 by 6 1/2 feet silk flags with painted devices for the regimental colors and perhaps the unit designation and battle honors (also painted) for the National colors. A good quality repor of these flags will be expensive if you want one produced exactly like they were during the war. Again Tom Martin or Steve Hill at Dupage Flags will be helpful to you. Both are excellent flag historians by the way.
Check the Order of Battle in Wiley Sword's book on this campaign and you wil see three Union brigades to chose unit colors from - McMillan's and Hubbard's of John McArthur's Divison and Moore's and Mehringer's of Couch's Division. Within these you will find troops from Minnesota, Ohio, Missouri,Indiana, Michigan and Wisconin - so a lot of flag possibilties for you.
Hope this helps.