I don't think African American schools were mentioned in the novel. Without a doubt Scout and Jem attended a segregated school even though it wasn't said. Schools did not become integrated until 1955 with the Brown vs. Board of Education Supreme Court decision. Even after that, the South was slow to integrate public schools. During the 1930's, black schools would have been poorly equipped and unequal to the white schools. In a rural setting like Maycomb, there was a pretty good chance they didn't exist at all. Many of the children would need to work on farms to help support their families.
There was one mention of literacy in the novel, and that was when Scout went to church with Calpurnia. Harper Lee wrote that there was little need for hymnals because only four people in the congregation could read. We can infer from Lee's description that many of the black people were illiterate at this time.