I have never figured out what made Flipper a hit show because in my eyes I think people loved it because Flipper was a cute dolphin and animal shows were becoming a thing after Mr. Ed debuted on TV. When my mom and I saw Flipper reruns on Nickelodeon in the 90's I think that Flipper was really the star of the show because I think he made the show have lots of adventures and as a dolphin lover myself I think dolphins are wonderful and I think METV should add Flipper soon because it was an awesome show. But why they remade Flipper in the 90's and also did a Flipper movie with Elijah Wood is beyond me because the remake of Flipper ruined the show and how the Flipper movie became a hit I'll never figure out

I think you mostly have it right. One other thing is that it was in color, and had a lot of beautiful ocean/underwater scenery. That was a big selling point in the mid-60s.