I took this from Jerome Walsh’s Style and Structure in Biblical Hebrew Narrative, Liturgical press, Minnesota, 2001, though it looks as though it was published before by Savran.
A. Solomon and the united Monarchy (1 Kings 1-11)
B. The separation of the the northern kingdom (1 Kings 12)
C. Kings of Israel and Judah (1Kings 13-16:20)
D. Civil war:the Omrid dynasty (1 Kings 16:21-34)
E. Elijah, the prophets, and the Omrids (1 Kings 17-2 Kings 1)
F. Elisha succeeds Elijah (2 Kings 2)
E’. Elisha, the prophets, and the Omrids (2 Kings 3:1-9:13)
D’. Civil war: the Omrid dynasty ends (2 Kings 9:14-11:20)
C’. Kings of Israel and Judah (2 Kings 12-16)
B’. The fall of the northern kingdom (2Kings 17)
A’. The kingdom of Judah alone (2 Kings 18-25)
Note: Walsh notes that the focus of the books is on the prophets and says “Hidden beneath an apparent historical account of kings and kingdoms lies the deeper story, the real story, of which political vicissitudes are merely epiphenomena: the story of the word of God and its bearers, around whom the true history turns”.