Diana Moon Glampers is definitely a flat character.  The main character in the books is Harrison.  He is the only one who attempts to change a society gone mad (other than possibly the ballerenia who joins him upon his coaxing), which makes him the only true round character in the book.  Glampers, though the main antagonist (unless you want to generalize the antagonist as society in general, which I personally feel should be avoided), shows no change throughout the book.  Her goal from beginning to end is to enforce the rules and maintain the status quo.  The reader doesn't learn anything about her other than what her job is and that she's diligent about following through with her duties.

I agree with my colleagues that Diana Moon Glampers is a flat character.

By definition, flat characters are less developed, often two-dimensional, and sketchy at best.

Nonetheless, these characters are still important to many works of literature. In Harrison Bergeron, Diana Moon Glampers exemplifies the evils of government control. While she looks average (much like Harrison's mother, Hazel), she is far from equal to the other citizens in the story. She, in fact, has power over everyone. Her character is in the story to show the inequality and corruption of a communistic society. So, while she is flat, she is definitely important to the story.

I located a site that has a pretty good chart (along with some other information) about round, flat, static, and dynamic characters that may be of some help to you.

Remember:

Round Characters are more fully developed

Dynamic Characters undergo change over the course of the story

Static Characters do not change.

Therefore, a flat character will likely NEVER be a dynamic character; since they are only the sketch of a character, they are never developed enough to undergo a major change of heart or experience growth like a round character can.

Interestingly, in many fairy tales and in some very short stories, there are NO round characters. ALL of the characters may be stereotypes with no real development other than their symbolic significance.

Diana Moon Glampers, the handicapper general, is a flat character. If she were round, the outcome of the story would have been totally changed because she would have likely had a change of heart, she would have relaxed the laws or else taken pity on Harrison and spared him his life. To the contrary, Diana undergoes no change throughout the story. She decrees the law, she enforces it, and when Harrison does not follow through, she executes him and the ballerina. There can really be no argument to the contrary here; Diana is flat.