Unlike, say, "The Weary Blues," we don't have jazzy rhythms and the catchy rhymes in "I, Too, Sing America." Instead, we've got short, deliberate lines that convey something that sounds a whole lot like quiet resolve. All those short, declarative sentences? Well, they're called "declarative" for a reason. And there's no hysterical language here, nothing that even sounds angry. It's just simple, like a statement of purpose. Which, when you think about it, is kind of remarkable. After all, the message being conveyed here is enormous: "we will be equal." Given what the institution of slavery looked like in the United States, that's a pretty stiff claim.
So when you read this poem out loud – or to yourself in your room – read it as if you were a teacher of sorts, calmly trying to explain something. Something that most people might think is impossible, but you know better. Use short sentences. And keep your voice even.