Kings Jehoshaphat and Ahab are both dead. We've finished I Kings and now II Kings and II Chronicles spreads out over the chronological timeline. The Blue Letter Bible (BLB) chronological reading plan lists Obadiah now, prior to beginning II Kings. Although this is disputed.
There is an Obadiah in Jehoshaphat's life and one in Ahab's. I never verified of they were the same one. It seems unlikely, as Ahab's was a trusted official and seems unlikely he would do that with a prophet from Judah.
As noted above, BLB lists this book here before II Kings. The NIV chronological bible feels there's evidence for a much later placement, as he seems to quote a Jeremiah prophesy and the destruction of Jerusalem. The Ryrie Study bible asserts that it is from an earlier time. Either way, it is a prophesy of doom for Edom as it comes against Jerusalem.
I figured I can read it more than once and see how it fits with what I've been reading.
Date: 840 B.C. or 586 B.C.