The fanciest stuff is heirloom sewn with pintucks, lace and embroidery. You use good cotton or Swiss Batiste.
None of that says anything about flammability. I dislike flannel sleepwear and blankets. All ours is cotton, broadcloth, batiste, or Tshirt fabric. I've used quilting cotton for shirts as I like to color block. I've used some for nightgown bodices.
I haven't seen any warnings for fleece, either. People use that for bathrobes.