Is it legal in the state of Florida to record your direct supervisor without his knowledge to prove hostile work enviroment?

As for recording audio, Florida forbids the recording of private conversations without the consent of all parties.  Violation of this law is a misdemeanor.  As for videotaping without audio, the law is more complex.  In general, using a camera in a public area without the other party's knowledge should not be an issue so long as audio is not recorded.  It gets trickier where a camera is used in a place or area where the other party has a reasonable expectation of privacy.  Obviously, a hidden camera in a locker room or bathroom would be a very serious concern and, in all likelihood, a violation of privacy under a number of legal theories.  Similarly, the owner of a property has the right to ban use of cameras.  Violating a ban or prohibition of this type could  be invasion of privacy as well as trespass and subject the violator to civil and/or criminal penalties. Finally, your supervisor may have a valid business purpose in asking you not to disclose your write-up to team members.  Unless there is a discriminatory or illegal motive to keeping the write-up confidential, the request seems appropriate.