The problem is this isn't true. Law's plan was to make kaido kill Doffy after messing up Ceasars operations, which isn't what happened. His goal had nothing to do with what actually happened in Dressrosa, which is the Marines arresting Doflamingo, and the beast pirates trying to save him. Kaido cares so much about Law destroying his Smiles..... that he, decided it would be a better use of his time to get drunk then capture him when he could
Meanwhile, he went out of his way to imprison Kidd and Killer, who never did anything to him, because his main goal in the arc was to recruit the supernova and Samurai, not to get revenge on the Luffy Law alliance.