Good to hear from you. No, the Book of the Annals of the Kings of Israel is neither Kings nor Chronicles (BTW, in the Hebrew Bible there is only Kings, not 1,2 Kings and there is only Chronicles, not 1,2 Chronicles) There are a few Jewish historical annals mentioned in the Old Testament. If you do some research, you will see that there were two or three others besides the one you mentioned. Samuel and Kings are historical records, and, as any good historian, the writer mentions his sources for his information. This gives us further reason to trust the historical reliability of the biblical histories. Joshua mentions the Book of Jashar, which is another annal. You will also find reference to another source, which is the Chronicles of the Kings of Judah (1 Kings 14:29 and 14 other references). All of these source annals have been lost, unfortunately.