FairMormon is a non-profit organization dedicated to providing well-documented answers to criticisms of LDS doctrine, belief and practice.
Source:Sorenson:Silk and Linen in the Book of Mormon:Ensign:April 1992
Sorenson: "At the time of the Spanish conquest, natives in Mexico would gather cocoons from a type of wild silkworm and spin the thread into expensive cloth"
Some people have wondered why the Book of Mormon mentions silk and linen (see Alma 1:29), since silkworms and linen as we know them were apparently not known in ancient America. The answer may be that even though the worm that eats mulberry leaves and produces silk in its cocoon seems to have been restricted to the Far East, several ancient American peoples had cloth as fine as and similar to silk.
At the time of the Spanish conquest, natives in Mexico would gather cocoons from a type of wild silkworm and spin the thread into expensive cloth. People in the Yucatan would also spin the silky floss from the pod of the ceiba tree (or silk-cotton tree) into a soft, delicate cloth called kapok. The silky fiber of the wild pineapple plant was also prized in tropical America, yielding a fine, durable cloth. The Aztecs made a silklike fabric using hair from the bellies of rabbits. Some cotton specimens excavated at Teotihuacan, dating to A.D. 400, have been described as even, very fine, and gossamer-thin.
As for linen, the flax plant from which the cloth is made was apparently not known in ancient America. However, several fabrics that look and feel like European linen were woven from native plants. The yucca plant and the leaves of the ixtle (agave plant) both yield fibers that make fine, linen-like cloth. A cloth made by stripping bark from the fig tree, soaking it, and pounding it also has some of the characteristics of linen. 
- John L. Sorenson, An Ancient American Setting for the Book of Mormon (Salt Lake City, Utah : Deseret Book Co. ; Provo, Utah : Foundation for Ancient Research and Mormon Studies, 1996 ), 232. John L. Sorenson, "Silk and Linen in the Book of Mormon - Book of Mormon Update," Ensign (April 1992), 62.