The intro should identify the title and author of the work in the first sentence and then provide a brief historical context (2-3 sentences) that establishes the setting in which the piece was written and the audience (non-racist, white Southern clergymen) that King was trying to persuade. Your lead paragraph should conclude with a focused thesis statement that directly addresses the prompt. I haven't seen the exact wording of the prompt, but I assume it asks you to analyze how King uses the 3 rhetorical strategies you identify to persuade his audience. I assume you understand what the 3 modes are, and I encourage you to think about King's use of "second-hand authority" (i.e. his implicit claim that his authority comes from God).
I assume that this is a short essay; if so, the body of your essay should devote one paragraph to each of the rhetorical strategies. You should start each paragraph with a topic sentence that both points back to the thesis and points down to how you will develop the paragraph. In the development of the paragraph, you should use quotes or paraphrases from King's text that correspond with the claim in your topic sentence and follow them with analysis that shows both how the strategy works and why King expects it to be effective with his audience.
Finally, you should write a conclusion that sums up your points and moves beyond, perhaps suggesting that this letter is important because King makes a moral and religious case to show that the civil rights movement is a righteous cause, so the audience of Southern clergymen will see that dismantling the Jim Crow system serves the will of the god that they have devoted their lives to.