Well, yes and no.
During the first two seasons of The Flintstones, the series was directed more at adults and had two main sponsors. At the end of the opening sequence when Fred turned on the TV, he was then on the screen promoting products from Miles Laboratories such as Alka-Seltzer and One-A-Day vitamins.
Later, when the show broke for commercial, the Flintstones would often be there as well, pitching still more products, such as Winston cigarettes. There were several different Winston ads where the Flintstones and Rubbles (as well as some supporting characters) sit around smoking Winstons and discussing the merits of the brand, followed by Fred singing the Winston theme song. During the closing credits, a Bedrock billboard could also be scene prominately displaying the Winston logo.
So, there was no actual cigarette smoking in The Flintstones episodes, but the characters did smoke in the sponsor ads. These ads are not included on any of the DVD releases, but can often be found on the internet.