JFK died on November 22, 1963. This man was born some time in July 1964, which means he had to be conceived in October 1963. Just barely possible, but even so, this story sounds like a crock.
Why? Given all the woman JFK was bedding, there has to be a number of illegitimate children out there. You would expect all that power and wealth to be able to keep the lid on it for a while, but not forever.