Dresser scarves are made to protect the surface of your furniture from scratches and wear. Embroidering a dresser scarf was one of the first things we did to learn our stitches and they went into our hope chests. I still have some I made 70 years ago and still use them.
A good source for linen/like fabric is Joann Fabrics. Some of their linen has polyester in it so does not require ironing. Comes in many colors and would be excellent for machine or hand embroidery. I have used it for years.
Carol J.