The speech needs a certain historical introduction, as it contains numerous references to the struggle against segregation laws in the 1950's and 60's, which students will problably miss otherwise. This lesson plan for a two-hour C1 class includes some reading, speaking and vocabulary tasks (1h 30'), based on extracts from the Wikipedia's page on the Civil Rights Movement, with a slide presentation to illustrate the major events of the movement and a clip from Bob Dylan's song "The Death of Emmett Till", which is mentioned in the Wikipedia texts. The second part of the class is a simple listening and reading task with a fill-in-the gap exercise on the transcipt of Dr. King's speech "I Have a Dream" (20'- 25'). The online file includes another document with further examples of Jim Crow laws. The lesson is hard at times but hopeful.
The text contains a lof of legal terms in American English. Some of the less frequent vocabulary students will come across is the following: facilities, [a court] to rule, literacy, to file a suit, a plaintiff, to overturn a decision/ a court ruling, a melting pot, to flirt, to dispose of, casket, to rally support, to acquit of a crime, double jeopardy, outrage, to spark, a standoff, a [lunch] counter, to pledge, bail, a restroom, to flee, to cram, turmoil, a stance, to enforce [a law], to skip school, restraint, upheaval, to gather, to fulfill [a requirement].
If you want further information on the March on Washington you can watch this Time Magazine short documentary (6':05") or just browse on Google or YouTube. The rally ended with some memorable musical performances by Joan Baez, The Freedom Singers, Peter, Paul & Mary, Mahalia Jackson, Bob Dylan, Odetta, or the Eva Jessye Choir, which are worth watching. Martin Luther King Jr. Day is a federal holiday in the USA which is observed on the third Monday of January (the 18th of the current month in 2021), as Dr. King's birthday was on January 15th.