Car trouble

Think of it like a kick scooter. You can walk, sure, but kick scooter is much more fun and faster, and one kick and it will roll for a distance. Flintstone car is the same way, they can stop running and the car can still roll for a distance.

You haven't actually watched the Flintstones then. They aren't sitting in that thing, they are standing upright with nothing to hold them up, so they can't coast at all.
- Watch it some more. They are chairs that their feet dangle out the bottom. The angle and drawing in the intro makes it seem like there's no seat. But in other scenes it's clearly there.
- Hmm you're right, granted the last time i watch flintstone is...25 years ago?
  But it still act like a cart and could hold stuff in that case.

This is the joke. How is this meme making fun of what is already clearly the intentional joke of the show?

This isn't even low hanging fruit, this is picking through the rotten scraps on the ground.

He runs while sitting. Somehow.

You ever seen a toddler in a cozy coupe?
My knees ache and my ankle pops just looking at them

That’s what always bothered me about those cars—let’s push all this shit in a sitting position when we don’t really need to! But also it’s a parody, so I’m takin’ the piss.

Actually, it does make sense to have a "vehicle" like this. We had them in real life, the precursors to bicycles were "dandy horse" and they operated by similar principles. Basically, the wheels of the vehicle allow you to "coast", maintaining the velocity you've built up with less effort.
The specific design of the Flintstones' vehicles is silly, yes. The posture is inefficient and the giant stone wheels would be a bitch to get up to speed. But that's just artistic license, IMO. You could build a four-wheeled version of the dandy horse and it'd be a reasonable vehicle for getting around in a place without any significant inclines.
- Actually shit yeah, that’s cool. Basically the same principles as a skateboard, really.
- Lol
It's because he's a quadzilla with undeveloped glutes. Explosive and significant short term power but incapable of extended endurance.

What bothered me more is the steering. How is that supposed to steer? The front wheel is just wedged into the frame.

He's American so there aren't any curves for him to worry about.
If he needs to turn at an intersection he could just pick it up like a trapbar and rotate.
There was only one road back then. Didn't need to steer.
- And it's 2d.
drifting with your feet
I always thought the steering wheel was wedged into the frame like everything else, so it basically bent the two anterior-posterior aligned pieces. That would look something like:
\
\ /____/
from the top. I can't really depict the way that it would bend the two rollers, but it would turn in a manner similar to the way the big fire engines with the rear and front steering wheels work.