The dated language probably reflects the fact that the translators of the KJV of 1611 relied heavily on the much earlier translation of the New Testament by William Tyndale published in 1526 with revisions in 1534 and 1536 (plus his incomplete translation of the Old Testament), often using its translation word for word. The KJV also drew on other translations like the Great Bible (1539), the Geneva Bible (1560), and the Bishops’ Bible (1568), themselves likewise indebted to Tyndale’s version.

A prominent example of his archaic language is his use of “thou” for “you.” “Thou” was falling out of use even in Tyndale’s early 16th century. See: [J. M. Pressley’s “Thous pesky Thou”] (http://www.bardweb.net/content/thou.html):

Thou was essentially extinct in standard English usage by the 1700s. One of the main reasons thou survives at all is Tyndale's translations of the Bible into English in the early sixteenth century. In his translations (for which he was condemned to die at the stake in 1536), Tyndale returned to the simpler convention of Old English, consistently using thou in singular usage and ye in plural usage. As Tyndale's work became the foundation for the King James version of the Bible in 1611, thou was preserved for posterity.

I don't think the KJV's archaisms are as much intentional as they are a matter of the older translations it relied on.

Maybe you are thinking about the Book of Mormon, which was written to sound like the language used in the KJ Bible?