What does this phrase from Chapter 38 of Maniac Magee mean: "For the McNabs, there was nothing free about public education"?
The phrase about which you are asking is actually found at the end of Chapter 37.
Russell and Piper McNab will only go to school if they are bribed, and thus "there (is) nothing free" about their education. As the author says, "a tuition (has) to be paid" for Russell and Piper to go to school, and "every week, Maniac (pays) it". In a twist on the usual meaning of the term "free public education", the tuition must be paid to Russell and Piper, not to the educational system.
The McNab boys are growing up in squalor and chaos. Their father is a drunk, their mother is apparently not present, and their house is a mess, with spoiled food everywhere and disgusting animal droppings on the floor. Russell and Piper, who are about eight, run wild, and their father's only effort to get them to advance their schooling is to holler at them, "Do you homework" as he goes out in the evenings and again when he comes home inebriated. Maniac, who despite his own lack of a structured upbringing, has a healthy sense of the value of education, and bribes the young McNab boys to go to school each week. At first, he offers them pizza to attend, but after awhile the Russell and Piper demand that he perform a series of heroic feats in order for them to go. Ironically, the amazing stunts Maniac does for the boys to get them to go to school provides them with something they sorely need, both in school and in their lives in general. The other kids now pay attention to them, "always crowding around, pelting them with questions" about what the famed Maniac Magee, who is living with them, is like. Russell and Piper are starved for attention, and the attention they receive because of Maniac makes them feel important for the first time in their experience. This importance, to the little McNabs, is "a wonderful thing" (Chapters 34-37).