I need to find an example of hyperbole in Up from Slavery, and I am confused on what that would be.

Hyperbole is an example of overstatement. It is characterized by the use of exaggerated language to heighten or further a rhetorical effect.
One representative example of of hyperbole is in chapter 15, when Booker T. Washington is describing his "Atlanta Exposition Speech" (in which he made some controversial pronouncements concerning how African Americans were to "deport themselves modestly" in order to achieve their political goals slowly and steadily). In this chapter, Washington expounds on the nature of public speaking by stating, "I think that one of the worst instruments of torture that was ever invented is the custom which makes it necessary for a speaker to sit though a fourteen-course dinner, every minute of the time feeling sure that his speech is going to prove a dismal failure and disappointment." He is clearly exaggerating for the sake of a comic interlude. Though he might disapprove of the time spent eating, surely he doesn't mind the meal itself!
In Up from Slavery as in other works of literature, hyperbole can be used for a variety of dramatic effects, both jarring and humorous.