According to Daniel Ludlow, the term "fine-twined linen" (Helaman 6:13) was evidently used quite extensively by the Hebrews; it appears nine times in the Book of Mormon and is used 32 times in the Biblical book of Exodus.
It is not clear what material was used to make the linen mentioned in the Book of Mormon. Hunter and Ferguson discuss this problem as follows:
The Book of Mormon makes reference to "linen," without qualifying it. It may be that the early Nephites had flax-linen. On the other hand, flax . . . was not found in America at the time of the Conquest. . . . The present scientific view is that linen from flax did not exist in ancient America. However, the word for linen would have been in the vocabulary of settlers coming from Jerusalem in 600 B.C. It occurs many times in the Old Testament. However, Bible scholars have suggested that the various Hebrew words that have been translated "linen" in the Old Testament are, for the most part, of uncertain meaning, and in some cases varieties of cotton are meant. In the United States today we sometimes refer to cotton products as "linen." Thus, perhaps the Nephites did not have flax, but rather used their word for "linen" in a broader sense. . . . The Hebrew background of the Nephites is reflected by its use.
[Milton R. Hunter and Thomas Stuart Ferguson, Ancient American and the Book of Mormon, pp. 316-317]