One might not have to look long before finding a reference. In the speech's first paragraph, King cites the Emancipation Proclamation. This document was signed by Abraham Lincoln, as King notes, almost 100 years ago (at the time of the speech, in 1963).
To reinforce the reference to this historical moment, King uses somewhat archaic language, like “five score years ago.” The immediate reference to history might have made the audience more aware of their context and tradition. It puts them and their anti-racist activism in conversation with past critical moments involving America and people of color.
A little later on in the speech, King states,
This sweltering summer of the Negro's legitimate discontent will not pass until there is an invigorating autumn of freedom and equality.
If one is familiar with the works of William Shakespeare, they might notice the “sweltering summer of the Negro’s legitimate discontent” resembles the first lines of Shakespeare’s play Richard III. The play begins with Gloucester/Richard III declaring, “Now is the winter of our discontent.”
For a third reference, think about how King’s dream that “every valley shall be exalted” relates to the Book of Isaiah. Also consider how King’s declaration that “we will not be satisfied until justice rolls down like water” links to a similar passage the Book of Amos.