Robbie: The term "jenny" is what carnys call a carousel, and "to
slough" is to tear down or dismantle.  So "sloughing a jenny" is
to dismantle the carousel to move it to the next town or date.

Bruce Pier

 [ Wow!  That must be old-time carnival jargon.  Gee, I was imagining
 [ you riding a burro, with your feet dragging on the ground (sort of
 [ like on the carousel. ;)   Thanks for the explanation, Bruce!
 [  -- Robbie