I haven't seen it in a few years, but esrogim used to come wrapped in flax. Or, at least, a yellowish, brownish, hairy substance people called "flax", which leads us to my first question:
This stuff would get everywhere. In particular, it would get on one's clothes, which leads us to my main question:
According to Shabbos 54a, this would not meet the requirements for shaatnez.
A double-fastening is needed to make flax and wool into a Kli.
One stitch holding a piece piece of wool to a piece of linen is not liable, two stitches are needed. Also, if you wrap a cord of wool and a cord of flax around your hand, you're are liable (eg. leading two camels, one with a wool leash and one with flax). Even though it is not held together with two stitches, you may knot the two cords together, and that would make you liable (even unintentionally).
Originally it was real flax. Then the major esrog growers in Israel found a way to save some money and switched to some other natural material. I don't remember exactly what it was Jute? or Hemp? I also don't remember exactly when the change took place, but I am sure it was sometime after 1980. Also I don't think that they went to the present packaging until around 2000. (From around 1955 to 1975 I worked on Canal St. right in middle of the "Esrog Center and was well acquainted with some of the major growers and dealers.
If the fibers are simply on top of the wool and not embedded, there is (are?) no kilayim; furthermore I'm not sure if a stray random fiber (as opposed to a thread) is considered significant. It seemed to me that SA YD 299:1 may be relevant, but I couldn't understand all of it.
