It is difficult to see any cultural similarities between these two great books, but I would argue that the similarity lies in the fact that both are related to the effects of war.
In "Civil Peace," the siege on Jonathan Iwegbu's home takes place in the aftermath of the Nigerian civil war, during which many lost everything. The book is set in a world in which all the characters are trying to rebuild their lives in the aftermath of this conflict. The war is also arguably why the robbers were quite as desperate as they were. This desperation is apparent in their willingness to accept a fraction of the money they initially demanded.
An American Childhood is a radically different story, set at the other side of the world in completely different circumstances. Our protagonist, Annie Dillard, is growing up during the Cold War, and she therefore finds the stories she reads about World War II highly relatable. Since she finds stories of war so interesting, I'm sure she'd have been interested in Iwegbu's tale of the Nigerian civil war, had she ever come across it.
I would also argue that Jonathan Iwegbu and Annie Dillard share another cultural similarity in their determination. While Jonathan is determined not to let the war dictate the rest of his life, Annie takes her love of art and music incredibly seriously, which is demonstrated by her playing musical instruments until her fingers bleed.