Let us remember that an epiphany can be described as a sudden insight or moment of understanding about oneself or one's situation in life. If we apply this definition to the story, we could argue that the characters who have locked themselves away in an attempt to try and cheat death and escape the virulent disease of the Red Death experience an epiphany at the very end of the story, when they are forced to acknowledge the presence of the Red Death amongst them and they realise that even the richest and most powerful of humans are incapable of cheating death. Consider the final paragraph of this powerful story:
And now was acknowledged the presence of the Red Death. He had come like a thief in the night. And one by one dropped the revelers in the blood-bedewed halls of their revel, and died each in the despairing posture of his fall. And the life of the ebony clock went out with that of teh lst of the gay. And the flames of the tripods expired. And Darkness and Decay and the Red Death held illimitable dominion over all.
This quote shows the way in which the story has come round full circle. Prince Prospero and his lords and ladies have moved from thinking that they can cheat death and lock themselves away in safety behind their castle walls to realising, with sudden horror, that actually death cannot be escaped or hidden away from. This is the central epiphany that exists in this short story.