Quite simply, the fact that slavery made it illegal (and severely punishable) for slaves to learn to read and write meant that oral tradition as a literary device was automatically integrated into their heritage. The only way to preserve and share knowledge was orally (with few exceptions such as Harriet Jacobs who wrote of her true life as a slave in Incidents in the Life of a Slave Girl but who published under the white pen name Linda Brent and was not given authorial credit under her own name until 1986!). This led to a tradition of very powerful Black speakers, such as Sojourner Truth, a former slave whose public speeches given on subjects ranging from abolition to women's rights appealed to both Black and White audiences.I have included a link to Alice Walker reading her most famous speech to give you an idea of why she was so popular!
The slave narratives, oral accounts passed down often from generation to generation, have given us the most accurate account of the Black condition during slavery. I have included a link to the WPA project that has preserved these narratives so that you can see just how compelling they are!
Additionally, the slaves used spoken word as a form of communication. Slave songs were often crafted to sound like "negro spirituals" when, in fact, they contained coded transmissions about escape possibilities.
This tradition stayed largely intact until the Harlen Renaissance brought about the first real emergence of a solid group of strong African-American writers. The depression stalled that movement, but it the momentum was picked up again in the 1960's during the Black Arts movement. While the written word became a part of the African-American literary canon, the spoken word still maintained power as is evidenced by the powerful speeches of Martin Luther King, Jr during the civil rights movement and the power of spoken word poetry of Amiri Baraka and Ntozake Shange today.
I believe that there are a couple of main reasons for this. First, there was the fact that most slaves were illiterate. Second, there is the fact that the black church has been a very important part of the black community and an influence on its culture.
Black culture in the US, of course, has its roots in slavery. As it developed, it was by necessity an oral tradition since few slaves were literate. This placed a premium on oral skills.
After emancipation, black churches became the backbone of the community. Sermons became something of a literary form, especially since many poor black farmers remained illiterate.
I believe this is why speeches are a part of the black literary tradition.