I've learned a few things.
First, the "I have a dream" sequence was improvised on the spur of the moment. What happened was that he he was several minutes into mostly reading his prepared text when the singer Mahalia Jackson, sitting nearby, said out loud to him: "Tell them about the dream, Martin. Tell them about the dream."
So on the spot he began to extemporize on the dream theme, which he'd used before. This shows an extraordinary ability to tune into his audience -- not just hearing Mahalia Jackson, but sensing the mood of the massive crowd.
He used the phrase "I have a dream" eight times to begin sentences. That's an example of anaphora, "the intended use of repetition that is applied to secure emphasis, to heighten the style, intensity, distinctness, or charm."
(In contrast, an epistrophe (or epiphora) is repeating words at the clauses' ends. The combination of anaphora and epistrophe results in symploce, a figure of speech in which a word or phrase is used successively at the beginning of two or more clauses or sentences and another word or phrase with a similar wording is used successively at the end of them.)
Anyone can use this device in speaking or writing, of course. It is indeed powerful, but so is dynamite. Better not play with it if you're not completely sure of what you're doing.
From the mouth of someone lacking King's skill, it can blow up in a face.
Another thing I learned: King was the 16th of 18 speakers that day! Huh? How many of the others do you remember?
Yeah, like that other guy who spoke at Gettysburg.