Consider reading some of King’s other works, especially collections of his writing and speeches, like A Call to Conscience: The Landmark Speeches of Dr. Martin Luther King, Jr. and A Testament of Hope.
There are several books that are set in the Jim Crow era that paint a picture of the national atmosphere at the time of King's imprisonment: Black Boy by Richard Wright, Go Tell It on the Mountain by James Baldwin, The Sport of the Gods by Paul Laurence Dunbar, Song of Solomon by Toni Morrison, and Invisible Man by Ralph Ellison.
Consider pairing “Letter from Birmingham Jail” with John Lewis’s graphic memoir March.
There are also a number of young adult books that might help students...