To whom is Martin Luther King speaking? Who is his intended audience?

Martin Luther King Jr. was a prolific speaker and writer, so it is difficult to give an exact answer because you have not asked about a specific speech or writing. That being said, often King's speeches and writings had a very diverse audience and he liked that because his entire goal was to bring both blacks and whites together. 

"Important in reaching King's enormous and diverse audience were the resources of black folk preaching. These...

Martin Luther King Jr. was a prolific speaker and writer, so it is difficult to give an exact answer because you have not asked about a specific speech or writing. That being said, often King's speeches and writings had a very diverse audience and he liked that because his entire goal was to bring both blacks and whites together. 

"Important in reaching King's enormous and diverse audience were the resources of black folk preaching. These resources included call-and-response interaction with listeners; a calm-to-storm delivery that begins in a slow, professorial manner before swinging gradually and rhythmically to a dramatic climax; schemes of parallelism, especially anaphora (e.g., "I have a dream that . . ."); and clusters of light and dark metaphors"

King often spoke to very large crowds of his own followers. For example, when he gave the iconic "I Have a Dream" speech, he was in front of approx. 250,000 supporters who had marched on Washington and met up at the Lincoln Memorial. This audience was predominantly black, however, all races were welcomed and many  non-backs attended. The speech was also aired on the radio and reached millions more people at home. So, his intended audience in this particular speech was incredibly diverse and his goal was to help not only his supporters see his point of view, but to present his "dream" to those who opposed him by putting a face on the oppressed and appealing to human values, not simply back or white values.