Question

Explain how Vonnegut uses flat, static characters like George Bergeron to develop his critique of 1950s American society

Answer 1

George Bergeron's character is, literally, extremely intelligent, strong, and capable. We know this because of the number of handicaps he is forced to wear by the government. His weights, for example, are so tiring that his wife suggests he risk removing them even thought the consequences are severe for doing so.
Because of his handicaps, George is a character who is incapable of changing, reacting to a situation, or even remembering what he his doing and he is such a rule-follower that he won't use his intelligence or strength to go against the government. 
A reader can see that the handicaps put on George are a metaphor for the burdens that the majority of the population of America are encumbered by in real life. While most people don't have pounds of bird-shot strapped to their necks, it is clear that people ARE burdened by great amounts of debt, jobs that pay little, stresses like large families, consumerism, etc that hold them back from participating fully in life. The "handicaps'' of the story are literally meant to show how much weight we are putting on the wrong things in our lives.
Vonnegut uses characters like George to demonstrate how little people are actually living. They are flat, unfeeling, unemotional, and unable to communicate, resist, or change. It is obvious that George SHOULD react to seeing his son's violent death broadcast on national television, but he is completely incapable of doing so because of the handicaps attached to him. The lack of character development, coupled with the excellent description of George's strengths due to his handicaps is what allows a reader to understand that the character is meant to be criticized. Readers are meant to ask themselves, how could he not react? How could he not remember? Why won't he question the ideals of the government? Why won't he risk himself for something that could save his son?

Answer 2

Vonnegut uses flat characters to exaggerate the lack of individuality that may result when a society seeks absolute equality. The fact that the characters are static emphasizes citizens’ inability to grow and change freely in a equal society.