What type of literary device does Atticus use when he says, "This case is as simple as black and white?" How is his word choice ironic?

The type of literary device that Atticus uses is a simile. A simile is a comparison using "like" or "as". He is comparing two opposite things in the phrase, "This case is as simple as black and white."
This phrase is ironic because Atticus is implying that the case is not difficult to understand. The facts of the case are not all that complicated, however the case is dealing with complicated issues. To many people in Maycomb, the case is simple. A black man raped a white woman. In the south at that time, there were no questions asked when an issue like this came up because of the heavy prejudices that were still prevalent. However, Atticus proves that the case is not all that simple. Throughout the trial, Atticus disproves Mayella's testimony with facts such as the bruises she endured could not have been made by Tom due to his injured arm. Atticus proves Tom's innocence, which complicates the trial. 
It is also ironic that Atticus uses this phrase because the case literally is about "black" and "white". Tom is black, and Mayella is white. Atticus is in a way saying that regardless what he is able to prove and do to help Tom, it will not matter because in the south, the word of a white woman would always be taken as truth over the word of a black man, regardless if it is the real truth or not.

Atticus uses a simile when he says, "This case is as simple as black and white"—he makes a comparison between two unlike things using the word as. This statement is also ironic, because Atticus uses the common expression "simple as black and white," which means that the case is not a difficult one to understand since there are no complicated facts. But in the reality of Maycomb's society, there is an issue that complicates the case, because Atticus's statement also implies that the verdict comes down to racial issues, as a black citizen has been accused, and a white citizen has brought charges.
There is no ambiguity in the legal case. Atticus has proven that Tom could not have caused the bruises on Mayella, because they were made by a man's left hand, and Tom's left hand is withered and useless. On the other hand, this case is not truly as "simple as black and white." The irony is that the case is complicated by being about a black man and a white woman, for a black man is accused of raping and beating a white woman in the Jim Crow South. And, at that time the word of a white person is taken over the word of a black person. In this respect, the irony of Atticus's statement is that the case being "as simple as black and white" means that it really is not so simple for the jury. For Atticus asks a jury of twelve white men to set a precedent and vote according to their conscience and reason, not their culture.