He was asked for both.
In fact the first movie came about because before then John and Steven did a movie called Always in 1989. John said the first time Steven had everyone together he said, "Ladies And Gentlemen i've found my Fred Flintstone." To which John groaned.
I don't know what happened the second time around, just that he was asked and turned it down. I don't blame him.
Did You Really Think You Could Call Up The Devil And Ask Him To Behave?-Fox Mulder, The X Files

I didn't know he was even asked. I thought the whole point was that the cast for this one needed to be younger.
Let Zygons Be Zygons.

Why? Because he heard yabbadabbadoo all the time on the street.
He didn't want to do the first one. He said he only did the first one because Steven Spielberg asked him.
But i agree he made a real good Fred Flintstone, and the first one was way better than the second.
They made fun of John refusing to do Flintstones in Vegas on SNL when John was boating.