However, there are a couple of things to consider:
* The Philosopher's Stone: Flamel mentions he and his wife have lived for 665 years. This suggests they have been using the stone to prolong their lives, which makes it possible that he could have died at some point after the events of the first book.
* Later Books: Flamel isn't mentioned again in the Harry Potter series after the first book. It is possible that he did die at some point later but that J.K. Rowling chose not to focus on this in the later books.
Therefore, there is no definitive answer to the question of whether Flamel died and, if so, when.