First, a general word about the KJV. Although a magnificently rendered translation for its time, the translators from the original Hebrew and Greek (and Latin...more on that later) who created this English translation had access to a small percentage of ￼the ancient Biblical manuscript fragments that translators have today.
This, in turn, means that we need to consider how Biblical translation is done in the first place.￼ It begins with ancient manuscripts that are the result of generations of hand-copying of texts. This copying was done by devoted scribes and monks throughout Jewish and Christian history, conducted over vast swaths of geography.￼￼
Because of human error and not any imperfections in God or His Word, some of the manuscripts contain errors or attempts at “helpful” theological explanation.￼ In certain geographic regions, where families of manuscripts developed, ￼￼such errors or supposedly “helpful” additions were copied repeatedly.
Over time, scholars have, as part of their desire to present God‘s word as accurately as possible, observed that some families of manuscripts have tended to repeat the same mistaken renderings of the original texts.
Part of the work of a prayerful translator is to determine which differences among families of manuscripts are significant enough to warrant exclusion from translation.
This is not a matter of adding or subtracting anything from the Word of God. This is a matter of attempting to render the Word of God accurately.￼￼￼
Those who produced the King James Version (KJV) of the Bible had a minute number of ancient manuscripts with which to work. For large sections of the scripture, they had no manuscripts at all. What they did them to produce their translation where they had no manuscripts was to consult the Latin Vulgate Bible, the official Roman Catholic rendering of the Bible at the time.
So consider that much of the KJV was an English translation of a Latin translation of manuscripts from the original Hebrew and Greek in which the Biblical writers composed their inspired writings. Beautiful as it is then, the KJV is a flawed and incomplete rendering of the Old and New Testaments.
Today’s translators have access to every extant ancient manuscript of the Bible there is, something like 10,000 manuscript fragments, from the third century-AD onward, for the New Testament alone.
So, if there are passages “missing” from these modern translations, it’s usually because the translators want to give you the actual Word of God and not what sometimes exhausted or helpful monks mistakenly included or excluded in translations like the Vulgate or the KJV.
My favorite current translation is the English Standard Version (ESV).
You might want to check out two of the following helpful books.
The Text of the New Testament: Its Transmission, Corruption, and Restoration (4th Edition)