The program follows the adventures of Fred Flintstone, Barney Rubble, Wilma Slaghoople, Betty McBricker and Dino as children as they deal with their childhood with their friends Nate Slate, Philo Quartz, and Dreamchip Gemstone while also contending with their bully Rocky Ratrock and his group consisting of Tar Pit, Flab Slab, Janet Granite, and Rocky's dog Stalagbite.

The premise of The Flintstone Kids, which depicts Fred and Barney as childhood friends with Wilma and Betty, contradicts the continuity of the original Flintstones series, which established in the episode "Bachelor Daze" that the two men did not meet their wives until they were young adults. Despite this, the character of Philo Quartz, who was created for this show, would later appear as an adult in the TV special A Flintstones Christmas Carol.

This series featured the following segments:

-The Flintstone Kids: The "main" story of the show. Either it would be the length of a full episode or be split into two different stories.
-Flintstone Funnies: Freddy, Barney, Wilma and Betty dreaming of exciting fantasy/adventures. These were dropped in the second season.
-Dino's Dilemmas: This segment featured the adventures and misadventures of Freddy's pet dinosaur Dino.
-Captain Caveman and Son: The adventures of Captain Caveman with his son, Cavey Jr. This segment was actually a "show within a show" whereby Captain Caveman and Son is a TV show watched by the main characters, with the "fourth wall" being broken frequently.