One could argue that Jankyn is under the shadow of confusion here; he doesn't realize that the only way to be successfully married to the Wife of Bath is to yield control to her in all things. The Wife has provided her audience with this information at the outset, telling them that her previous husbands "moste yeve it up as for the beste, / Or elles hadde we nevere been in reste" (433-434). They knew how to achieve the peace and accord that is at the heart of a proper comedic outcome; what's wrong with Jankyn?
What's wrong with Jankyn is that he's oppressed by the dark shadow of medieval misogyny. This misogyny tells him that he should be the most powerful person in the marital relationship. It prompts him to read horribly antifeminist proverbs and stories to his wife, probably in the hope of putting her in her place. But Jankyn doesn't understand the Wife's character, or that she will never yield to him.
Perhaps finally understanding the Wife's true character, or maybe deciding that he's tired of arguing, Jankyn yields completely to the Wife (at least according to her). This decision brings about the accord that is the goal of comedy. In fact, claims the Wife, after this she "was to hym as kynde / As any wyf from Denmark unto Ynde / And also trewe, and so was he to me" (829-831), and that after that day, they never argued again. The burning of the Book of Wicked Wives could represent the vanquishing of the misogyny contained therein. Whether or not we think that this fight with Jankyn actually went down as the Wife describes it, or that it's just the Wife's fantasy verbalized, it represents the ending of comedy as it's meant to be.