Paul does not wear a rose to his office,even though the second job that he gets in the story is that of a clerk. The only time where Paul wears any flowers in his lapel during the story is when he goes to the teachers' board with his High School headmaster to discuss his bad behavior.
During that specific instance, he wears a red carnation. He wears this to show flippancy and carelessness, not to mention, superiority towards his teachers. The problem in this particular instance is that the teachers are sick of Paul, and the feeling is reciprocated.
The red carnation is considered offensive by the teachers, since a meeting with the headmaster is far from an occasion to get "dressed up" for. Hence, Paul challenges "the system" by wearing his red carnation to a possible expulsion meeting.