Is Ranked MMR and Ranked Flex MMR the same?

Since they are different queues and you are allowed to queue with people more than 1 division above you, you can safely assume that they have different MMR systems.

For the fact my solo queue mmr is gold 1 and im playing with diamond (solo queue ranked) people because my flex rank is p5 yes its different, however my flex rank is around their flex rank as well