Looks like in 2027 we might see the transcript of the audio recording (King with prostitutes) or hear the actual tape.
The documents are thus not slated for release until 2027.[5][6] Among these are an FBI file called “MURKIN” (for Murder-King, the official designation of the Martin Luther King assassination investigation)[7] and information about how the FBI, through COINTELPRO, targeted King while he was alive.[8] Due to known FBI policies, many of its records may be destroyed before that date, thus leaving many questions about the King assassination unresolved.[9]
https://en.wikipedia.org/wiki/Martin_Luther_King_Jr._Records_Collection_Act
Following up:
This is a balanced and well-researched response to the allegations in the FBI file:
The alleged audio recordings will be released in 2027.
Make what you will of the veracity of the FBI report.