Answer: He finds Albus Dumbledore's famous wizard card from a Chocolate Frog on the Hogwarts Express and remembers it later when the trio are trying to find out who Flamel is. On the card, it mentions that Dumbledore worked closely with Flamel. When Harry says so, it triggers Hermione's memory and she proceeds to take out a massive book she'd borrowed from the library for 'some light reading.' In it, it states that Flamel is the only known creator of THE SORCERER'S STONE, which can be used to make the Elixir of Life. USing this, Flamel and his wife were stated to be 600-something years of age. (P.S.: at the end of the book, Dumbledore tells harry that he and Flamel decided to destroy the Sorcerer's Stone because it caused too much trouble (cough Voldemort tryna steal it cough), so Flamel dies in his 600s in Paris.)
Explanation: I literally just finished reading the book like yesterday