Provide three examples of allusions that King uses to support his reasoning. How does this type of evidence strengthen his argument?

Dr. King uses an allusion when he refers to the Reverend Reinhold Niebuhr, an American theologian and professor as well as a leading intellectual during the mid-20th century. Niebuhr wrote several influential books, one in particular that addressed the morality of the individual versus the immorality of society. He is also credited with writing the Serenity Prayer. Dr. King writes,

History is the long and tragic story of the fact that privileged groups seldom give up their privileges voluntarily. Individuals may see the moral light and voluntarily give up their unjust posture; but, as Reinhold Niebuhr has reminded us, groups are more immoral than individuals.

This reference to such an eminent person—one who has actually been called the greatest Protestant theologian in the last two centuries—strengthens Dr. King's argument and credibility with his intended audience, a group of white, Southern religious leaders. Not only is he familiar with Niebuhr's work, but he is also influenced by it, as they likely have been as well.
Dr. King employs another allusion when he refers to the common drug, thalidomide. He says that black Americans are often told to wait, as though waiting will eventually result in there being a good time, so to speak, for them to demand their rights. However,

This 'wait' has almost always meant 'never.' It has been a tranquilizing thalidomide, relieving the emotional stress for a moment, only to give birth to an ill-formed infant of frustration.

Thalidomide was a drug used to treat anxiety and other kinds of tension as well as morning sickness in gestating women. Sadly, thalidomide causes terrible birth defects and many thousands of infants were born with malformed limbs, among other problems, as a result of their mothers' ingestion of the drug while pregnant. Many of these infants could not survive. Here, Dr. King continues to show his own intellectual capacity and the extent of his knowledge, referencing what would have been a very well known issue of the time, something sure to grab the attention of his audience and give them pause, make them think about how the black community has been placated only to have even bigger problems later.
Dr. King employs another set of allusions when he writes that

You express a great deal of anxiety over our willingness to break laws [...]. Since we so diligently urge people to obey the Supreme Court's decision of 1954 outlawing segregation in the public schools, it is rather strange and paradoxical to find us consciously breaking laws. One may well ask, "How can you advocate breaking some laws and obeying others?" The answer is found in the fact that there are two types of laws: there are just laws, and there are unjust laws. I would agree with St. Augustine that "An unjust law is no law at all."

Here, he alludes to the Supreme Court ruling in favor of desegregation, Brown v. Board of Education. The highest court in the land has ruled that desegregation of schools must take place but a black person still cannot sit at the same coffee counter as a white person? He also alludes to St. Augustine, another important touchstone for the religious community. In making these references, Dr. King both establishes his knowledge of the law as well as his knowledge of what is right. The idea that one does not have to obey an unjust law is not his own but is grounded in religious authority and sacred texts.

An allusion is a reference or connection to something else. Using an allusion connects what a person is writing or speaking about to a different event, place, person, or thing, and this helps put their topic into a specific context for the reader or listener, helping the audience connect, intellectually and/or emotionally, to what is being said or done. The type of allusion used might have to do with the audience. To an audience of children, you might make an allusion to an experience they are familiar with, like learning to ride a bike or being forced to go to bed early. To an audience of religious leaders like Dr. King's, he makes allusions to religious and historical people and events he expects them to know about and have strong connections to.
Dr. King uses allusion in his letter to compare what he is doing to important historical people and events, putting his own work into an important historical context. Three examples are as follows:
1) "...just as Apostle Paul left his little village of Tarsus and carried the gospel of Jesus Christ to practically every hamlet and city of the Greco-Roman world, I too am compelled to carry the gospel of freedom beyond my particular hometown."
2) "Isn't this like condemning Jesus because His unique God-consciousness and never-ceasing devotion to His will precipitated the evil act of crucifixion?"
3) "It was 'illegal' to aid and comfort a Jew in Hitler's Germany."
In all these cases, Dr. King is referencing important historical people and events he expects his audience of Southern preachers to understand and have certain associations with. He uses references to Christian heroes and recent terrible events to appeal to his audiences' knowledge of and emotions about these people and events. In doing so, he compares himself and the people he is working with to people he knows his audience will be sympathetic with, appealing to their morals. He also places himself in an important historical context, elevating what he is doing as important work.

Allusion is used many times throughout Dr. King's letter. Here, I will point out just three:
1. "just as the Apostle Paul left his village of Tarsus and carried the gospel of Jesus Christ to the far corners of the Greco Roman world"
2. "Just as Socrates felt that it was necessary to create a tension in the mind so that individuals could rise from the bondage of myths and half truths to the unfettered realm of creative analysis and objective appraisal"
3. "It was "illegal" to aid and comfort a Jew in Hitler's Germany."
In all three cases, Dr. Martin Luther King Jr. uses allusion to cast his struggle in the terms of historical significance. By drawing comparison to events that most people are familiar with, he makes the argument that what he is doing is monumental, something to be written down in history books for generations to come.
Let us also remember his audience: the letter begins by addressing "My Dear Fellow Clergymen." Dr. King was a Baptist minister, and his allusion to the Apostle Paul invokes the sacred oaths that he and his readers have all taken. He reminds them of their collective similarity in a time of drastic segregation, and he calls forth their allegiance to justice and truth.
Finally, Dr. King was a realist. He understood that his task in writing this letter was to induce sympathy in the unsympathetic and to make his cause and struggle a common one. His allusions to Socrates and Hitler's Germany remind us of a lesson history repeatedly teaches us: to exist as a responsible member of society is to question its traditions.