what is the difference between flexibility analysis and stress analysis?

What is your background? Are you a Mechanical engineer?

Most mechanical engineering curriculum in India does not teach Finite element method ( some colleges offer it as an optional course) or Structural analysis and hence "flexibility analysis" appears to be an alien term.However based on a course on Strength of Materials which you must have taken, I do expect that you should have understood the context in which Flexibility analysis has been used.

I would advise you to read any standard text book on Structural analysis or on Finite Element analysis and yes pl. don't start working on CAESAR before you get these concepts cleared.

Regards