What is the purpose of the dream at the end of the story Battle Royal?
It seems clear that the grandfather's deathbed warning combined with the narrator's grueling battle experience has unsettled the narrator; his dream contains information about life's beginnings and endings, and the knowledge he now carries about his life as a black man.
The grandfather's refusal to laugh at the dream circus clowns seems to symbolize the seriousness of the narrator's situation. Graduation from high school is a milestone, usually a time for optimism; for the narrator, instead, it is a mirthless time. Graduating from childhood to adulthood means accepting the full weight of society's treatment of black men.
The envelopes the narrator dreams himself opening are symbolic of the endless endurance tests he has been put through, and will be put through as he ages. Like the "battle royal" of the previous evening, the narrator must perform a number of arbitrary tasks for permission to do what he wants to do, to achieve anything greater for himself. (This unending rabbit hole of envelope-opening seems to reference Booker T. Washington's "politics of respectability" argument.)
We can only guess Ellison's purpose in using a dream sequence to comment on these themes. Perhaps he means to highlight that a black man's agency can be taken away from him even in the subconscious, so punitive is society's judgment.