Mac Flecknoe is the poet-king of the realm of nonsense. After many years as ruler, however, it comes time for him to step down. Ultimately, he chooses his son Thomas Shadwell, a poet of unparalleled dreadfulness, as his successor. Shadwell is the worst writer in all the land, and thus, the perfect man for the job.
Upon arriving in the city of August (a.k.a. London), Shadwell is crowned king of the realm of nonsense. Mac Flecknoe himself delivers a brief speech on his son's merits (or lack thereof) during the coronation.
At this point all the action pretty much stops, as the poem devolves into a thinly-veiled, full-force condemnation of Shadwell's writing and character by the speaker. In the end, crowned and ready to rule in his father's footsteps, Shadwell is poised to sink poetry to an even lower level.