This song came out in 1933, and has been done by various artists, notably including Ella Fitzgerald and Nat King Cole. I've cited the Bobby Darin version (which came out in 1966) because the submission form is still not set up to cite a proper decade for performances before the 1950s or after 2009. I know what a honky-tonk is, and I know what a parade is. But mix the two, and I draw a blank on what the term might mean. I've looked up "honky-tonk parade" and most of the hits are for this line in this song. So this song seems to be the origin of the term and offers no explanation therein as to what a honky-tonk parade might be. The principal exception I found to those hits is a song named "Honky Tonk Parade", written and recorded by Billy Gilman. Billy Gilman wasn't born until 1988. So however clever his song may be, it is at best an attempted explanation after the fact when it comes to trying to explain a baffling phrase in a song that first came out in 1933. In fact, Gilman's song makes several references to things all predated by any 1933 song, including Disneyland, Spiderman, and Snoopy.