Narrating in the style of the third-person omniscient narrators of classical epics like The Iliad and The Aeneid, we soon realize that our speaker actually refers to himself in the first person, briefly inserting himself in the story (check out lines 25-32). This speaker seems earnest at times, and totally tongue-in-cheek at others, but certainly does his part to propagate the opinion that Shadwell is as bad a writer as they come.
But let's be real. Sure, when talking poetry, it's never a good idea to mix-up the author and the speaker. But in this case we have to say that the speaker is pretty much just John Dryden. He pokes a bit of fun at his own expense, even referring to himself as a "dunce" (31). But this dose of self-deprecation occurs for the sake of irony; we get the sense that he doesn't take himself too seriously, unlike, say, Shadwell. For, ultimately, we get the sense that the opinions the speaker shares are Dryden's own. We know he was extremely critical of many of his contemporaries, and skeptical of the cheap, unimaginative nature of many of the day's popular poems and plays. "Mac Flecknoe," it seems, is at least in part Dryden's clever way of critiquing not just Shadwell, but the entire English literary scene.