Just curious if that cat was ever part of the family, because he was Fred's nemesis in those closing credits. Yet I don't recall seeing him in any episodes.
The cat, who was officially named Baby Puss, was shown in only 2 episodes.
Season 2, Episode 15 - The X-Ray Story:
Wilma is trying to feed Dino, who is too sick to eat. Wilma says to Dino, "If you're not going to eat this, I'll give it to the cat." Baby Puss is then seen running out the door.
Season 5, Episode 4 - Pebbles Birthday Party:
In the beginning of the episode, Fred's snoring is keeping everybody up including the cat (who is sleeping in Fred's bed). Baby Puss eventually lifts its head and says, "I am going to the animal shelter where a cat can get a good nights sleep."