Is it correct to use "most" + "-est" together?
No it is not ok to use more + -er or most + -est, unless you want to sound childish.
Cambridge:
Warning:
We do not use more or most together with an -er or -est ending:They emigrate because they are looking for a better life.
Not: …a more better lifeThe beach at Marmaris is one of the biggest in Turkey.
Not: …the most biggest…
Not "OK". If you want to go "over the top", then it should not be with a grammatical error but rather using extra (or arguably extraneous) adjective(s):
Welcome to the absolutely, positively wildest show on earth.