What was the normal flight path for a passenger aircraft from New York to Miami in 1955?
Probably not a whole lot different than today. You likely won't get a very exact answer to a general question like that unless you can narrow down specifically what kind of detail you seek. 

Obviously GPS waypoints wouldn't have been used, but any NDBs in use at the time probably would be. My advice would be to search for a vintage chart from that era and plot the most direct route using depicted navaids.