In my stash of course! mwahahahahaha!!
But seriously, fabrics do seem to come and go. Rayon may be one of those that's gone these days, unless you have a stash like mine.
Regardless, what you're going to be looking for is a lightweight, natural fiber. Polyester won't pleat. Also avoid fabrics with lycra or spandex in them for the same reason. Unfortunately, I feel that quilt cottons don't work well as broomstick skirts--the fabric is a too tightly woven and heavy, resulting in a stiff, board-like skirt. That's a shame, really, because they have some great prints and colors.
As your humble correspondent, I decided to do some searching around to see what's going on these days. Since my local fabric stores are Jo-Ann, Hancock's and Hobby Lobby, I've become familiar with ordering on-line. If you can't find rayon in a local store, this could be an option for you as well. These are some on-line stores that have rayon or other fabrics you could substitute:
fabric.com: Most of their rayons are batik, but there are also some rayon failles you might try.
Fashion Fabrics Club: 33 pages of various rayon fabrics. Not all would work, such as suitings, linen look and knits. But there's bound to be something usable in that many pages. Not especially responsive but the prices are good.
eQuilter: Batiks, hand-dyes, prints. Lots of tropical shirt type prints, but the search also brought up some pretty bamboo and cotton blends. I haven't tried using bamboo for broomstick skirts, but they'd probably work, being natural fibers and all.
Textile Studio: Not much rayon, but they have some pretty silks, cotton lawn and cotton voile. These types of fabrics would work. From my experience, they are responsive to email questions.
Gorgeous Fabrics: Not much woven rayon, but Ann has some silks that would probably work, cotton gauze, cotton voile, and also some rayon velvet devore that would be fabulous. Not to mention a huge assortment of rayon knit that would make great coordinating tops for your skirts. Ann, the owner, has always responded quickly to my questions.
Emma One Sock: No rayons that would work but her stock changes often. Try back again.
Waechter's: Mostly rayon batiks at this time but there are a few rayon prints mixed in there. Also cotton lawn and voile. And silk.
FabricMart: I didn't see a lot of rayon this visit, but it's a good resource and worth checking often.
If you have additional suggestions, let me know and I'll add them to another post.
Warning--it's very tempting when searching all these websites for fabric. So of course, a few pieces are on their way to Casa Flan. These may or may not be broomstick skirt worthy, but I'm sure I'll find a use for them.
This one is coming from Gorgeous Fabrics:
These two are from Textile Studios:
Don't say you haven't been warned.