Fred has violent sneezing caused by an allergy. To stop the sneezing, he goes to the drug store for a bottle of "Scram." Each such pill stops a fit of sneezing, but has the side effect of turning Fred temporarily into an ape.
Fred borrows money from Mr. Slate to fix up his backyard for a long weekend. He plans to spend the whole weekend in Bedrock with his family and the Rubbles. But Gazoo invites the Rubbles and Flintstones to spend the weekend in the 25th Century A.D. instead. Among the many marvels they encounter: a descendant of Mr. Slate who still wants back the money Fred borrowed that weekend, plus interest.
At the races at Hollyrock Park, Fred and Barney wager on dinosaurs picked by the Great Gazoo. Gangsters take note of their success and kidnap the two friends so that they can make winning picks for them.
Traveling through the desert on their way to Rock Vegas, Fred and Barney fall prey to con men who have seeded the river with phony gold. When it turns out that the river contains real gold after all, the con men will do whatever it takes to oust the Flintstones and Rubbles from their claim.
When Fred chooses bowling over taking her to a ball, Wilma calls upon a rich, dashing old boyfriend to escort her to the ball instead. Fred ultimately decides to crash the ball later in the evening, escorting his own date--Barney, transformed into "Barbara" by the Great Gazoo.
The cavemen and their children meet "Dripper," a dolphin-like sealasaurus and star of a show at a marine park. Dripper is the target of an abduction plot. Thinking they have Dripper, the kidnappers instead abduct Barney, who's dressed in scuba gear.
Overhearing Wilma telling Betty that Dino has aristocratic ancestry, a member of the country club assumes it's Fred who's being spoken of, and invites the Flintstones to become members. Fred knows he's in need of polishing, but when the evening of the big event at the country club arrives, he and Wilma have an inspiration: go as themselves and show the snobs how to have a good time.