The parade starts back by the safari and winds around the park finishing in the same place it started. If you can grab a seat by the Island Merchantile you can head over the bridge and out the entrance as soon as the parade passed. Just be aware that everyone else will have the same idea and it can get pretty jammed trying to get out right after the parade.
I like to watch at the beginning of the parade and then hop on the safari or grab a seat in the shade between Africa and Asia, somewhere around flights of wonder, and see the end of the parade with no crowds.