If there are any still flying 707s, and I truly believe that there are, find somebody at the Miami International Airport (MIA) because that is where they will most likely be. However, I am also sure that they have been modified the same as John Travolta's 707.
A lot of 707s were modified at the Santa Barabara (SBA) Airport to comply with FAA regulations. You might contact some one there, I cannot find the name of the company that does the modifications.
Good luck.
One more thing, a bit off topic, but tell the producers that when they have Navy pilots in uniform on the program, make sure they wear Naval Aviator wings on their uniforms. A pretty bad omission for a show that has done a very decent job of period accuracy so far.