Hmm, you are in Illinois, but where is the baby? If up north you might want that batting.
Since I haven't personally done this in years, my inclination would be to try it with scraps and see what happens. I know I don't have to change any tensions on my machine when I go from sewing to quilting. Though flannel usually has a bit more give than cotton, such that you might want to use your walking foot anyway and avoid any puckers on the back.
Maybe someone else has more recent experience or advice.
ali