Stone Age (10000 BCE to 2000BCE)
The Flintstones is supposed to be the Stone Age when man was using stones as tools. It lasted from about 10000BCE and 2000BCE when metalworking began.
Though dinosaurs was also present in the movie so using some other thoughts we can also say it is from Prehistoric Time.
If we combine both the thoughts the movie is prehistoric + stone age time...
Enjoy the confusion...