Dumbledore didn't help create the Philosophers Stone with Flamel- he only worked with him on some undisclosed alchemy projects. As you've already suggested, for Flamel to live long enough to work with Dumbledore, he would have had to have been using stone long before Albus was born.
For reference- the Chocolate frog card that mentions them working together has this text:
Considered by many the greatest wizard of modern times, Professor Dumbledore is particularly famous for his defeat of the dark wizard Grindelwald in 1945, for the discovery of the twelve uses of dragon’s blood and his work on alchemy with his partner, Nicolas Flamel. Professor Dumbledore enjoys chamber music and tenpin bowling
