Nicholas Flamel dies at 666 years old. "Mr. Flamel, who celebrated his six hundred and sifty-fifth birthday last year enjoys a quiet life with his wife, Perenelle."

He then destroys the stone later that year. Assuming the time it takes get his affairs in order will be within a year or so, he'll have likely died at 666. 

That's the coincidental/superstition side of this magical world I love. A lovely little Rowling-esque detail.