Abstract from Kingdom of Priest - A History of Old Testament Israel by Eugene H. Merill p. 346

The chronology of the stories of Elijah is extremely difficult to re-construct but the reference to Jehu and Hazael would suggest that they were persons already known to Elijah. Jehu, however, did not become king until 841, twelve years after Ahab's death, and he reigned for twenty-eight years. It would seem, then, that Elijah's commission came late in Ahab's life. We know also that it came at least four years before the king's death. The basis for this assertion is that the commission was given before Ben-Hadad's siege of Samaria, which in turn was four years before Ahab was slain in the Ramoth Gilead campaign of 853 (1 Kings 20:1, 26; 22:1). A date of 857 for Elijah's trek to Horeb would appear to be reasonable. Since that journey was after the three-year drought, Elijah must have first encountered Ahab in about 860, fourteen years after he had commenced his reign. This would be ample time for the apostate conditions described in the narrative to have taken firm root.