Martin Luther King Jr uses the Boston Tea Party in his speech in order to make a connection between the current Civil Rights movement and the origins of America. During this time, African-Americans who protested or practiced acts of civil disobedience were often looked down upon by some white citizens. However, Martin Luther King Jr. argues that in order for change to occur, there needs to be some ways in which people express their discontent with the current system.
By discussing an event that many Americans are familiar with, he is drawing up a comparison so that people can relate to the actions of African-Americans during this era. This shows that blacks in America are fighting for a better life, just like the American colonists did when dealing with the British government.