Most everything about him in MoR, except for the part where he's immortal, lines up quite well with the historical figure: he published his findings regarding the Philosopher's stone, diagrams included. Of note is that the supposed real-world philosopher's stone did not immediately give Flammel the results he wanted; according to the book published in his name, some years passed between him getting it to transmute silver and getting it to transmute gold.

Historical Flammel also has an official grave site in France (Paris, if I remember correctly); I want to think he lived to his eighties, but it's been a few months since I last read about him.

The book-supposedly-by-Flammel mentions a mysterious old mage that helped him along the way; I would expect myself to go "SQUEEEE!" if it turned out Flammel's mysterious old wizard got mentioned in HPMoR.