I do have a friend that did a series of embroidery. She spun up various types of wild silk, then embroidered a picture of the moth that created the silk. Very neat stuff and they did an article for it in Spin Off.
Cotton is a short fiber and it's hard to spin it as fine as you need for thread. It likes to be spun fine, but still hard to do. That's why I'd go with silk or linen.