There are thin, lightweight batting’s that are recommended for wearables, but you can use flannel if you want to. It would be your choice to use just pieced outer and flannel or to use a third layer lining. Either way is fine, just depends on what you prefer .
as lar as the sleeves better quilted or not- again a personal choice. I would quilt them mainly because it’s going to ensure they don’t get ( baggy- out of shape) when the jacket is laundered. Same with quilting the back. I think you would want to stay with the same for the complete jacket- either batting or flannel, either lining or not.
silk, bamboo and wool are all nice lightweight batting’s, although the wool is loftier. And there are cotton weights that say they are recommended for clothing. I live in a cold climate so I would use batting and maybe a flannel lining but any way you choose is your personal choice, there is no wrong way to go. I hope you show us your jacket when you get it finished.