Silk is mentioned several times in the Book of Mormon such as in Alma 1:29:
And now, because of the steadiness of the church they began to be exceedingly rich, having abundance of all things whatsoever they stood in need—an abundance of flocks and herds, and fatlings of every kind, and also abundance of grain, and of gold, and of silver, and of precious things, and abundance of silk and fine-twined linen, and all manner of good homely cloth.
This was always seen as problematic as it has long been held that silk was unknown outside of China until the late second century BC.
However recent discoveries have shown that silk was indeed available in Mesoamerica:
Wild silk was used until recently in some areas of Oaxaca. The species that produced it appear to be Gloveria psidii, a moth, and Eucheira socialis, a butterfly, both of which are found in midaltitude, relatively dry forests. In Santa Catarina Estetla, a Mixtec community in the mountains west of the Valley of Oaxaca, a wild silk called, in Mixtec, doko tachi was gathered from oak trees and spun and woven into very durable sashes. Wild silk was also used to weave sashes in Santo Tomás Ouierí and other communities in the Zapotec area of Yautepec; two types of wild silk were known in this area—one found on oaks, the other on madrona trees (Arbutus). A silk gathered from oaks is also remembered in San Miguel Cajonos, a Zapotec community in the Villa Alta district.– Alejandro de Avila B., “Threads of Diversity: Oaxacan Textiles in Context,” 125.
Not only was silk available in Mesoamerica but other materials which could also be described as silk were also available too. Why would Joseph Smith take such a chance on using a material thought to be anachronistic?