You leave the papers in while you sew them together, the papers add the stability. Once a piece is completely surrounded you can remove that paper. And yes you reuse them over & over. I have paper pieces I've been using for 20 years.
Play out your flower; stitch the six pieces around the center, pop out the center piece, keeping the outside papers in place. If you are adding a ( path) around the flower add those pieces then you can remove the flower papers. Keep going, as you put your ( flower garden) together you just remove papers as they are surrounded. So when the top is done you only have pieces around the outside. Then you can remove those when no more pieces are added.