Nicholas and Perenelle Flamel were targets for most of their lives because of the Stone; it might make them unaging and immune to nearly everything else, but there were still a few ways they could be killed. So whenever they got sick of it, they did their own little witness protection program and set themselves up as new Hogwarts students. This time around, they chose to be James Potter and Lily Evans (which...needs an explanation for Petunia. Still a relative, maybe, but not a sister.). But somewhere along the way, Dumbledore learned who they were, and either set them up or just capitalized on their deaths to steal the stone.