Hi,
That is really lovely, a nice print and great style. It looks very much like silk, or a fabric imitating silk. Is it slippery, or does it have a texture when you run your hand over it? Is it a bit stiff feeling, or is it more limp? Does it stand up on its own? If it is not silk, my guess it is a blend of rayon and acetate, or possibly all acetate or some other post war synthetic.
If you can snip off a few threads or a snippet from the seam allowance or hem, then do a burn test, that will tell you if it is silk, rayon or a true synthetic. It could even be a silk rayon blend, but the burn test will determine that.