Many sources conclude that the FBI have documentation of MLK's adultery, and many sources conclude that he was an adulterer.
All information comes from the FBI and filtered through Lyndon B. Johnson. Consider the atmosphere of the country - there was a civil rights movement taking place and J. Edgar Hoover was extremely fervor in his collection of data on everything ranging from Communists, Terrorists, and Activists. Former President Harry Truman stated:
Hoover transformed the FBI into his private secret police force. Truman stated that "we want no Gestapo or secret police. The FBI is tending in that direction. They are dabbling in sex-life scandals and plain blackmail. J. Edgar Hoover would give his right eye to take over, and all congressmen and senators are afraid of him".
"God-----it, if only you could hear what that hypocritical preacher
does sexually." -Lyndon B Johnson
LBJ, the President during the Gulf of Tonkin Resolution,
reviewed all of the material the FBI collected on Dr.
Martin Luther King, Jr. It was found during the FBI's searches for communism and surveillance on civil activists.
According to Time Magazine, yes, the FBI taped MLK's
extramarital affairs.
Shortly after Johnson took office, the transcript and tapes of Martin Luther King's bedroom activities were spirited to him. He read the accounts, which an aide described as being "like an erotic book." He listened to the tapes that even had the noises of the bed-springs.
Michael Eric Dyson's book, "I May Not Get There With You: The True
Martin Luther King, Jr.," concludes it is widely known that King
was a womanizing adulterer. Again, Dyson comes to the leader’s
defense. He asserts that the reformer’s “relationship with Coretta
symbolizes the difficulty faced by black leaders who attempted to
forge a healthy life with their loved ones while the government aimed
its huge resources at destroying their families...”
The author agrees that MLK had an extramarital affair - and the US Government had its hand in a smear campaign against him.
Of course we have the "Suicide Letter" itself:
FBI Agent William Sullivan, one of Hoover's deputies,
"apparently took it upon himself to write the anonymous letter and
sent an agent to Miami, to mail the package to Atlanta," Beverly Gage
wrote in the Times. William Sullivan was a leader on COINTELPRO under
J. Edgar Hoover, providing counter-intelligence towards many civil
rights activists.
Conclusion
It is extremely plausible that MLK was indeed an adulterer, and that the FBI has evidence of such activity. The article mentioned below can help sum it all up best:
The Hollywood Reporter article, "Selma and the Sex Tape Controversy," reveals:
Garrow says exactly what material the FBI "included on the 'highlights' reel is specifically unknowable," but that both scripts take their own liberties with the truth. "I acquired a pretty detailed understanding of what was on the surviving tapes," says Garrow. "It probably was King on the tape," says Chuck Fager, King's colleague and Selma jail cellmate.