Today's "King James-only" movement, and its argument that the KJV is itself inspired, does indeed have historical precedence, though it's debatable if the 20th-century movement can claim a strong link to similar thinkers in previous centuries.

There are two major precedents to today's movement, so we'll look at those first:

• Pre-KJV elevations of particular translations (Septuagint, Vulgate, and Luther's Bible)
• Nineteenth century elevation of the KJV
• Late 20th-century KJV-only movement

Pre-KJV

Before the KJV was completed in 1611, several other translations of the Bible enjoyed particularly high status, with some groups going so far as to identify them as inspired in and of themselves. Three frequently cited examples are the Septuagint, the Vulgate, and Luther's Bible.

The elevation of the first, the Septuagint, dates back as far as 100 BC, in the Letter of Aristeas. Much of the letter is rejected as fictitious, but it does describe supernatural guidance in the writing of the Septuagint, and a curse laid on any who dared edit it. In the early first century, Philo describes how all the translators of the Septuagint independently came to have the exact same text:

They, like men inspired, prophesied, not one saying one thing and another another, but every one of them employed the self-same nouns and verbs, as if some unseen prompter had suggested all their language to them. (Works of Philo Judaeus, III, 82)

Philo's account influenced early church fathers like Justin Martyr and Irenaeus, and they defended the accuracy and even inspiration of the translation.

Much later, in 1546, the Vulgate was similarly recognized by the Council of Trent, which said that "no one is to dare, or presume to reject it under any pretext whatever." When Erasmus published his own critical Latin text, he was opposed by Martin Dorp and Petrus Sutor (a.k.a. Pierre Cousturier), the latter of which said:

If in one point the Vulgate were in error the entire authority of Holy Scripture would collapse. (Quoted in Preston and Jenkins, Biblical Scholarship and the Church, 27)

And similarly, some advocates of Luther's German translation of the Bible, completed in 1534, considered it inspired:

Some indiscreet friends of the reformer, impressed by the beauty of the translation, imagined they could recognize in it a second inspiration. (History of the Reformation, III, 337)

So we see then a very early tendency to elevate particular translations, and thus it shouldn't surprise us that something similar happens in English.

KJV onlyism in the 19th century

The KJV enjoyed dominance in the English-speaking world for many years after its publication, and was not seriously challenged until the 19th century, when the Revised Version was prepared. This new translation was not undertaken without major debate, during which the "inspiration" argument was adopted by many opponents of a new translation. Many authors briefly note the existence of such arguments, such as:

• Henry Alford, 1866: "Yet this is the version which some would have us regard as infallible, and receive as the written word of God!" (Commentary on Hebrews)
• Around 1840: "Some had gone so far as to pronounce the Bible as translated by the distinguished forty-nine, a perfect work!" (Life of Spencer Houghton Cone, page 355)
• Armitage, 1850: Some "hinted" that the KJV "had come down from heaven in about its present shape, printed and bound" (History of the Baptists, I, 901)

Thus the idea of perfection of the KJV itself has existed for a long time, at least as early as the mid-19th century.

KJV onlyism in the 20th century

Roy Beacham and Kevin Bauder, opponents of KJV onlyism, provide more historical details than I have, and conclude that "no traceable connection exists between those of the nineteenth century who held such a view with those of the later part of the twentieth century" (One Bible Only?, 44) They find the modern movement's origin to a book published in 1930:

That book, Our Authorized Bible Vindicated, was written by Seventh-Day Adventist missionary, educator, and theologian Benjamin G. Wilkinson (1872–1968).

Wilkinson opposed the English Revised Version, Beacham and Bauder say, because "it robbed him of several favorite Adventist proof texts," but his book was uninfluential until it was discovered by James Jasper Ray, who published a derivative work, God Wrote Only One Bible, in 1955. And this work, in turn, inspired David Otis Fuller and Peter Ruckman, two highly influential KJV-only proponents. Ruckman's The Bible Babel (1964) and Fuller's Which Bible? (1970) both rely on Ray, and in 1978 Fuller founded the Dean Burgon Society to promote KJV onlyism. Both argue that the KJV is an inspired translation and absolutely authoritative, and Ruckman has bombastically claimed that the KJV has new revelation, above and beyond the original scripture.

According to Beacham and Bauder, all notable KJV-only proponents, like Jack Chick, D. A. Waite, Jack Hyles and Gail Riplinger can be linked "back to Fuller or Ruckman or both," though they admit the existence of at least one scholar loosely associated with the movement, Textus Receptus proponent Edward F. Hills, who was uninfluenced by them.

Conclusion

The history of the modern KJV-only movement can be traced primarily to Benjamin Wilkinson and his 1930 book. But to do so would ignore a long history of claims of inspiration for the KJV and other translations, stretching back as far as the time of Christ. As the Oxford Handbook of the Bible in America says:

As an identifiable entity, the King James Only movement is rather young, overwhelmingly Baptist, and thoroughly American. While its ideological roots stretch back to nineteenth-century Britain and the first calls to revise the KJV, the movement is properly a product of the second half of the twentieth century. (source)