there is no such thing as wrinkle resistant linen. There are various blends with some linen in them that look a little lineny but that do wrinkle less. You need wool in the blend, though, not silk.
I would look at drapers. I used to know of one such cloth that Logsdail loved but I forgot what it is. I think it was linen-cotton-wool or maybe linen-silk-wool, anyway, it was a blend of three fibers.