It's a question that always get asked...can I use cotton for my clothing at Renaissance Faire? The short answer is no...and yes. The Renaissance people of Europe were familiar with cotton cloth. It was in existence, but it was rare and expensive. Keep in mind there were two types of "cotton", one, the cloth we know as being made from the fibers of the cotton flower, or boll, and then there is another made from wool. "Cotton" can also apply to a cheap and thin woolen cloth being made in this period as well. So there are two "cottons" you as a historical reenactor can use. One would be the real thing...but your impression should be one of wealth and privilege as cotton was imported from India and Asia, thus expensive to purchase. It would not have been called "cotton", but "calico". Second would be the inexpensive woolen cloth called "cotton", and you could use plain old wool flannel that is a little on the thin side to represent that type of cloth, as this cloth was loosely woven, light, and very fluffy to the eye and touch...mush like modern wool flannel cloth.
I would suggest that any sort of cotton that had block-printed patterns (essentially a wood block that was inked and applied to the material) would be extremely rare outside of the Orient. "Chintz" as it was called, probably did not show up in Elizabethan England. It is predominantly seen in common usage from the mid 17th-century, forward...that would be the middle of the 1600s up to today, well out of the Elizabethan Era. So how do we explain this portrait?
This is a 1568 portrait of Sir Henry Lee, and well within the early Elizabethan period. I direct you attention to his shirt. That is block-printing, and it has been applied to a fine quality linen. At this early date I suspect it's not cotton, and it is not embroidered as the pattern is too perfect. He is a man of means and wealth, as a shirt like this would be costly, but not as much had it been embroidered. a "blackwork" shirt with this much needlecraft...priceless, and out of sight for all but the most wealthy.