The showers are downstairs in the main departure area, below the stores that they have on that level. Just follow the yellow signs...they're very clean due to the fact that there's like 2 people in there constantly cleaning both the showers and the restrooms.
Originally Posted by themicah
The Mercure is where the showers for KL plats are.
But IAH_Flyers is correct that there are public showers in the restrooms on the corridor somewhere between the non-Schengen KLM lounges. I forget where exactly, but I seem to remember them being near the BA lounge.
The public showers are totally open to the public. Like IAH_Flyer said, there are no amenities or anything, but if you bring your own towel (and a plastic bag to put it in afterward), the showers are super clean and those bathrooms are almost always deserted, since nobody really goes up there unless they're going to the lounges, and the lounges have their own bathrooms.