How to unclog kitchen sink drain from coffee grounds (?)

My kitchen sink drain is running very slow and I think it might be blocked with coffee grounds because that's what's coming up when I use a plunger on it.

I don't have a snake but I'm sure I can borrow one. It's just that the drain hardware is plastic and I don't want to risk breaking it. (I mean the part inside the drain cup where you fit the stopper. The pipes are plastic too but they're sturdy.)

Is this a good case for using liquid drain unclogger chemicals?