A "stanky booty" means a "stinky ass." A stanky booty is an ass that hasn't been
washed recently, and therefore it smells of
doody, or poop. And ass perspiration only adds to, or increases the
funk!
Please note that one can pronounce the word "booty" as "boo-tay," for an added touch of refinement, or a mark of personal distinction by the speaker.