For an animated show that relied heavily on cartoony slapstick, I nonetheless can only recall one instance where spanking played a part in an episode. This occurred when the wives, Wilma and Betty, disguised themselves as men (i.e., put on big fake moustaches) in order to sneak into the Water Buffalo Lodge where Fred and Barney were members to see just what they did at their meetings. Unfortunately for the ladies, they get caught up in an initiation ceremony, and both ladies wind up getting swats from a paddle as part of their induction.
Thankfully, what a TV series neglects, more often than not fan fiction and fan art jump in to fill the void. Here are some renditions of the spankings that never took place, but should have--and Happy 50th Anniversary to The Flintstones!