I do have a feeling that the Flamels might die, the series is called the Secrets of the Nicholas Flamel, so I think that might be that when he dies, the secrets he held will be revealed, and that might have something to do with the story. I'm just not sure when, I mean each story if you think about really takes place over just a couple of days. So I don't think they'll die of old age, because the average book takes what, 3 days? If he had 30 days at the beginning of the series, at the end of 6 books, he would have about 12 days left. So IF he dies, it would have to be by other means.
I also have a theory that Flamel actually is with an elder, I remember several times this is mentioned, "Flamel never tells anyone the whole truth." maybe he might be with an elder, just not formally serve him/her.