You are correct - cotton flannel is largely incorrect for the period. What WalMart calls "double nap" is actually a bit closer to "sanded twill" cotton than what we see sold as cotton flannel (like that in long sleeve modern flannel shirts). The "double nap" actually is a tighter weave and courser appearance than modern cotton flannel. It is still not a perfect choice to replicate garments with, but is closer fit to make citizen's shirts than to try to make Federal issue shirts with.
Moderator and Sewer of Historical Clothing and Tall Tales
"But our opportunity to learn and grow, to communicate the richness of the lives that have gone before us, that does not change. We do not outgrow it. It does not tatter and fall apart in our hands..." -Mrs. Terre Lawson, 2010