There is only one narrative point-of-view in Black Boy by Richard Wright; the novel is written from a first-person perspective from the point-of-view of the author and narrator, Richard Wright.

One way the novel could be considered to have two points-of-view would be to contrast the tone of young Richard and adult Richard. Young Richard understands things from a child's perspective; the book opens when he's four, and the memories he has are colored by his perception during that time period. For example, he might not recognize things that an adult would easily recognize—such as burning some straws from a broom could end up causing a larger conflagration. Adult Richard has the same understanding as any adult and is who he is because of those childhood experiences.

You can also look at the difference between the point-of-view of Richard the writer and Richard the narrator. The author has the perspective of someone who remembers the past and can understand it through the lens of his experiences. For example, Richard the narrator as a young child doesn't understand why they can't make the cat live again after it's dead. Richard the narrator understands that his father telling them to kill the cat was demonstrative of his personality.

Richard Wright, a genius author and fantastic storyteller, utilizes a first-person narrator in this novel.  What is unique, though, is that he is able to make his narrator the only real character.  Others are not elaborated upon and Wright presents them in only enough detail in order to give the reader an idea of how they affect him, his actions, etc. He is able to let the reader focus ONLY on the narrator's experiences living in a world filled with racism and hardships.  The reader does not, then, get side-tracked by interest in other characters.  He presents a narrator who is living in the Jim Crow system.  eNotes explains:

This narration demonstrated the principles of living within the Jim Crow system which Wright had previously laid out in "The Ethics of Living Jim Crow," published in Uncle Tom's Children. He represented these ethics through the didactic story of Black Boy with the intention of altering white America's racism. Wright believed that a well-developed protagonist in a successful novel would do more for race relations than any political speech or ruling. Therefore, by the use of his own experience re-enforced by a first person persona, Black Boy exposes the reality of life for the black American realistically but without offering solutions.