It was mentioned that he became a king 10 years ago.
15 years ago Vergo became a marine on Flamingos behalf - Vergo was always part of Flamingos Crew. So it could very well be that Flamingo was roaming as a free and normal pirate till 13 years ago (he might have become a pirate right after Rogers execution which he witnessed) and became a Shichibukai at the same time as Hancock.
So the theory that the Shichibukai were founded because of Flamingo is not really unvalid - it still remains a possibility. There is so little we know about this institution itself that you might consider it because of Flamingos heritage and the standing of the CD. About Hancock becoming a Shichibukai - I know.
It's a really dumb idea, the instituition is clearly higher purposed than one friggin guy.