"The Scripps Library, through cooperation with various presidential libraries, has been collecting some of the most important presidential speeches in American history. These speeches all have transcripts, and some are available in their entirety in audio or video." From the Miller Center for Public Affairs at the University of Virginia.
The document search is called OKRA. Under Advanced Search, type "King" in the Search by Author. Click Filter by Genre, choose Speech from the dropdown menu, and click Go.