Totally epic, bro. Much of the poem's success depends on Dryden's ironic use of the kind of elevated diction and grandiose imagery typical of the epic genre. All this epic-ness makes the decidedly not-so-epic subject matter (read: Shadwell) seem even lamer by comparison. This ironic juxtaposition is the basis for the "mock-epic," and one Dryden's main satirical techniques.
Lines 1-4: Dryden kicks off the poem with an epically grandiose philosophical commentary. Of course, as we know, this ain't The Iliad; it's Mac-freaking-Flecknoe. This mock-heroic tone established in the opening lines ends up driving the rest of the poem.
Lines 43-44: Throughout "Mac Flecknoe," Dryden references numerous classical myths and epics, reinforcing the mock-heroic tone. Flecknoe and Shadwell are frequently compared to these heroes of old, beautifully contrasting the complete and total ineptitude of our own heroes.
Lines 94-97: Personifying fame epically as an "Empress," who spreads around town news of the new king's coronation, Dryden satirizes Shadwell's sense of self-importance. Dryden jokes that Shadwell is known all the way from Bun-Hill to "distant" Watling Street—in reality, two very close places.
Lines 112-115: Dryden compares Shadwell to the legendary Carthaginian general Hannibal, joking that the writer is like a great warrior, bravely defending his kingdom against an onslaught of enemies. He does so in his father's stead, like many princes.
Lines 216-217: Dryden greatly admired contemporary English poet John Milton, whose epic poem Paradise Lost deals with the divine struggle between God and Satan. Perhaps it's no coincidence that he concludes "Mac Flecknoe" with a Biblical reference of his own, to the story of Elijah and Elisha. With this passage, Dryden pays homage to Milton's unique epic style, while taking a shot at Shadwell's emphatically mortal origins.