Okay so as the old fan theory goes:

Lord Voldemort represents the first brother who asks for a wand more powerful than any other. Of course, that power proves to be his downfall.

Severus Snape represents the second brother, who asks for a tool to resurrect loved ones, and gets a stone from Death.

Harry Potter represents the third brother, described in the fable as a humble man who only asks to live a long happy life without the fear of Death. In the fable, Death bestows an invisible cloak upon the third brother, which protects him (but not his brothers) from his end. So Harry Potter is the boy who cheated death, makes sense, right?
The Dumbledore Theory
Death searched for the third brother for years, and was only able to find him after the brother gave his cloak of invisibility to his son. When Death shows up, the third brother greets him as an old friend and went off with him gladly, “departing this life, as equals.”
So what harryjxmespotter adds to this old fan theory is the suggestion that Professor Albus Dumbledo represents Death in this fable.

Its a fun fan theory at very least. I don’t believe that Harry Potter author JK Rowling has ever talked about the possible allegories. She has said that The Tale of the Three Brothers is loosely based on Geoffrey Chaucer’s The Pardoner’s Tale, but it also feels partly inspired by Three Billy Goats Gruff.