No way it is linen or polyester.Look at the thickness of the collar and the way the coat hangs, It is bulky and that comes from wool. No othr fabric gives that lay and fold.
My wife won a `Sewing with Wool’ award many years ago. I asked her to look at the photo of Shrillary.
She doesn’t think it’s wool: “Too thin, it looks like some kind of jersey fabric.”
Whatever jersey fabric is ... Satan’s satin?
Whatever it is, she’s got something under it. I still think it’s inflatable bloomers to compress her loose caboose.