I did have on hand some synthetic fabrics from my grandmother's stash that she probably used as linings. I tried this and it worked much better. Here is a blue flower I made out of that:
I used a brad from my scrapbooking stash for the center.
I also discovered that one of the scarves I picked up at the yard sale was synthetic and would work so I managed to get two flowers done. I will admit I stitched them together and did not like them and cut more circles and had a second go. This particular fabric curls VERY EASY and will shrink up half the original size- so I've learned not to cut my circles too small. Here are my flowers. One has a vintage jewelry piece for a center and the other has some pearls I stitched in.
And what about the silk chiffon that I can't use for this? They became these:
The one on the left is made from this tutorial and the right one was made by folding the circles into quarters and stitching them together at the bottom points.
Check back because I plan to work all of the white flowers into some jewelry pieces.