In Lord of the Flies, how does William Golding use Roger and Jack to show that the disorder they have created will lead to more disorder?
This is a great question. A primary theme in William Golding's Lord of the Flies is that when human nature does not have any restraints or authority, it devolves into savagery; Jack is the first to display savagery when he paints his face and loses all sense of shame and conscience. Roger is also one of the older boys, and he is one of the characters who most displays that the savagery on the island will only get worse.
Roger is surly and angry from the beginning of the novel, and his disposition only grows worse throughout the course of the story. He deliberately destroys the littluns' sand castle and throws rocks at one of the boys, missing him only because he still feels some of the restraints of the civilized world in which such actions are not acceptable.
By chapter eleven, though, Roger is the cruel second-in-command of Jack's tribe, and we have evidence that Jack would have been ousted--or worse--if the boys had not been rescued. Jack scolds Roger for not being on watch as he was assigned, and it is clear that, unlike the others, Roger is not particularly intimidated by Jack and his painted-face authority.
Roger edged past the chief, only just avoiding pushing him with his shoulder. The yelling ceased, and Samneric lay looking up in quiet terror. Roger advanced upon them as one wielding a nameless authority.
Jack's authority, at least over Roger, is not as strong as it once was, and the indication is that Roger is willing to get physical with Jack if necessary.
When Ralph is on the run from Jack and the other savages, he finds Samneric who warn him that the others, particularly Jack and Roger, are trying to kill him.
“You don’t know Roger. He’s a terror.”
“And the chief—they’re both—”
Clearly Roger is the worst terror, based on the twins' recent experiences with the tribe. Before Ralph leaves, they warn him that “Roger sharpened a stick at both ends.” This indicates that Roger intends to put Ralph's severed head on a stick like the Lord of the Flies, an act which Jack initiated last time and goes far beyond a simple murder.
The boys, led by Jack, are responsible for creating a deadly disorder; Roger's actions and attitudes at the end of the novel indicate that even more death and disorder would have followed if the boys had not been rescued.