I'm tempted to say an Electra-Glide, but I have no proof. I don't believe the Electra Glide was introduced until 1965. These were probably either Hydra Glides or Duo Glides. EDIT: At least one commentator has identified the bikes as 1963-1964 Harley FL Duo Glides. http://www.paulseaton.com/jfk/acoustics/houston/Speed.htm
Okay, so let's take this off the "unknown" list.