Martin Luther King Jr was trained in composing and delivering sermons. One device he uses is prediction: he announces, in advance, the organization of what he is about to say. Locate examples of prediction in "Letter from Birmingham City Jail."

King was a master rhetorician, and that was a key part of his successful organizing for Civil Rights. He was able, especially, to appeal to whites so that they would support the cause of black equality.
Some places where he states in advance what he is going to say—using prediction—are the following:

In any nonviolent campaign, there are four basic steps: collection of the facts to determine whether injustices are alive, negotiation, self-purification, and direct action.

This is a basic use of prediction. He employs a topic sentence that expresses the four points he plans to cover. Further, this prediction keeps the focus where King wants it to be, which is on the non-violent aspects of his campaign. This prediction makes his readers aware of his disciplined devotion to peaceful agitation for change.
A slightly different use of prediction is as follows:

I am sure that each of you would want to go beyond the superficial social analyst who looks merely at effects and does not grapple with underlying causes.

This both indicates (predicts) that King will be looking deeper in this letter than simplistic analysis and is also a persuasive tactic. It flatters the intelligence of his readers and brings them into his circle of people who desire to see and understand more.

You may well ask, "Why direct action, why sit-ins, marches, and so forth? Isn't negotiation a better path?" You are exactly right in your call for negotiation.

The above quote again both appeals to his readers—"you are exactly right"—and predicts what he is going to talk about, which is his understanding of how oppressed groups arrive at serious negotiation.