I would like to clear up the question a little bit. Round and dynamic are synonyms of the same type of character. Both refer to characters that change from the beginning of the story to the end of the story. Flat and static both refer to characters that typically remain the same and unaffected by the events throughout the story.
I would say that the most dynamic character in The Outsiders is Ponyboy. That makes sense, since he is the main protagonist and the narrator of the story. It would be a fairly boring story, if the narrator never changed. Pony's attitude about the Socs changes because of the events in the story. At first, Ponyboy sees the Socs as just a bunch of wound up rich kids looking for a fight. But through characters like Cherry and Randy, Ponyboy comes to see that the Socs are people just like him. They have a different set of problems, but problems none the less. Speaking of Randy, he also would be a dynamic character, because his entire attitude of the gang war changes by the end of the novel.
I think the best example of a static character is the Soc, Bob. He's just a jerk through the entire story. I would like to make the argument that Johnny is a static character too. Johnny has been changed drastically because of the beating that he received from Bob, but that happened before the events of the book take place. The reader learns about Johnny and his change in a flashback sequence, so I would say that Johnny is static throughout the events of the book.