re: How do those wing flaps slow down a commercial airplane...

I’m assuming you mean the fully lifted spoilers when the plane is on the ground....in which case you are right, they aren’t a major contributor to slowing down (although the higher drag helps).

Their main purpose is to reroute airflow through the wing so that lift generation is negated (“lift dump”). It’s part of why when the plane is on the ground, it stays there hard rather than coasting down.

Also, as it quickly makes the wings carry less weight, it increases the efficacy of the brakes.

But mostly it’s a safety feature, to keep the plane stable on the ground before activating the primary initial slow down method: thrust reversers.

Kinda.... spoilers are a lot more important than TRs

In terms of getting the plane down, sure.

It’s a lot easier to land a plane with busted thrust reversers than no spoilers.

But not in terms of slowing down.

Outside of the aforementioned increase in brake efficiency at least

They don’t slow the plane down. They slow the earth’s rotation.

While some (a couple) of the reply's are technical and most are snooty I'll try and give you a middle of the road answer. The flaps create air drag (drag slows you down)(kind of like that time you where in Miami and thought the hot girl was hitting on you. Then your true friends pointed out it was a guy in "drag" which cooled your engines.) Same principal action. The direction that the flaps are in (up or down) determines if there is lift or downward force. Too much of either could be bad which is why pilots go through training.

At the end of the day the simple answer is science and stuff. Hope this helped.