Most likely he came East Tennessee for industry, in particular the boom of the timber industry which happened around the turn of the century. There is an online article from the Tennessee Encyclopedia where the author writes about Northern Soldiers coming back after the war. "Soldiers passing through the state during the Civil War frequently commented on the verdant natural resources, particularly in the eastern part of the state; some of these men later became investors and entrepreneurs in the turn-of-the-century timber boom." The full article is here Tennessee Encyclopedia.
This article led me to the discovery of the Flanders Lumber Company of Roane County which was listed as having incorporated In the American Lumbermen publication in 1906. There isn't a Henry Flanders listed as an owner but there is a CP Flanders along with a few other men. Maybe this might give you some direction in your search. I would be curious to know if these men served with him and if he came thru Roane County or East TN at any point during the war. Here is the link for the American Lumberman publication. This should take you to the exact page but if not it is page 65 and is in the far left column, 3rd paragraph, under Tennessee heading.
I hope these shed some light on your quest for an answer.
Fun side note: In the 1940s Roane County became the center of the war effort, as the Secret City, Oak Ridge, was brought into existence.
