Silk charmeuse is good, or just a plain weave silk - I agree that it doesn't look very shiny. A silk-cotton blend might also work.
The skirt looks gathered to me, but there's not much skirt being shown in the image.
Actually in the pipes:
- Remaking Ser Loras doublet.
- Luke Skywalker, A New Hope
- Wind Waker starter costume in swim material
Eventually: Paul from Dune, Faramir, Harry Sullivan