Is the history of Israel’s kings recorded in the OT/NT all there is we have on those kings? O r is there significant Israeli history we should know outside the biblical narrative that can help our faith?
The Old Testament is the most thorough and reliable source of historical information from the ancient world–especially of the Near East. Before the fifth century BC there were no real historians producing histories, at least in the modern sense. Before the Greeks Herodotus and Thucydides, the first systematic historians, most “histories” were extremely one-sided polemical works, written to glorify the leaders in power in that area at that time. The amount of reliable historical information we have from writers before the Greek historians, other than the OT authors, is relatively limited. We do have a significant amount of archaeological evidence from the ancient world, but the historical evidence available to us is less. For this reason, we have little to no historical information outside the Bible for the Near East during Old Testament biblical times.
Actually, this is a bit of an exaggeration because from Herodotus and later historians, we do have record of the time of the Babylonian and Persian kings. so, if you are talking about the Old Testament after AD 600 or so, you will find some useful historical information to compare to the Bible. For example, Herodotus gives an account of the destruction of Babylon in 538 BC which agrees, more or less, with the biblical account of the same event in Daniel Ch 5. There is information about the history of Persia available from Thucydides and Herodotus which confirms the historical accounts in Ezra with regard to Darius, Cyrus, Xerxes and Artaxerxes. But this is after the period of the kings, which is what your question is about.
Also, we know from the books of Samuel and Kings that there were historical sources available to the writers of the Old Testament, such as the “Annals of the Kings of Israel.” But these sources are lost to us.
Let me give you some examples of archaeological rather than historical evidence which supports the reliability of the Bible. We have archaeological finds, such as the Taylor Prism (which verifies information about King Jehu), the Lachish Letters (which confirms info about the time of Hezekiah), the Tel el Amarna Letters (which support the conquest under Joshua) the Cyrus Cyllinder (which agrees with the biblical account of the conquest of Babylon), the Moabite Stone (which mentions Ahab of the House of Omri) or the Tel Dan inscription (which confirms the reality of David, Omri and others). All of these provide significant information that corroborates the biblical history from the period from about 1400 to 500 BC, but we do not have the writing of historians from this time period. So, if you want help for your faith, you should look more to archaeology than to history. I have quite a bit of information on this topic available at the web site. Here is one link you might find helpful: https://evidenceforchristianity.org/history-archaeology-and-the-bible-updated/ I also have quite a bit of info on evidence for the historical reliability of the Bible in my book “Reasons for Belief” (available at www.ipibooks.com)
If you look into this subject, I believe you will conclude that the historical and archaeological evidence supports the reliability and inspiration of the Bible, but it does not prove it.