There are numerous conflicts in Rodman Philbrick's Freak the Mighty. First, Max is very uncomfortable with who he is (both internally and externally). As a large boy, he is very uncomfortable with his size (compared to others his age). He is also uncomfortable with his own person (given his father's imprisonment).
Kevin also faces conflict. He has a growth condition which keeps him very small. Like Max, this bothers Kevin both internally (how he feels about his size) and externally (how he looks on the outside).
As Freak the Mighty, Kevin and Max face an external conflict--Tony D. Tony D does not like the boys and goes out of his way to cause trouble for them (even chasing them into a lake at one point). Max also faces his kidnapping by his father (another external conflict).