Hmm! Mine is a Y stamp. I suppose for lack of a better word, if not "plasticky", it's sort of similar in texture to treated lambskin or goatskin like a Chanel 19 bag. It's not as porous as untouched leather, it feels like there's a bit of gloss. It was somewhat matte when I first got it and I wonder if my usage/hand oils have made it shinier? In terms of "thinness", I'm just comparing it to Chanel flaps and totes, which may not be a good comparison since I think they put board or something inside to give it more structure. I've never actually seen a B/K up close in person and none of my friends own any B/Ks so I have nothing to compare it to.This sounds like a very sad first world problem!
I appreciate any input!

Here is a photo of my Kelly it's an X stamp. This may not be helpful, but I get what you mean my bag developed a sheen the more I used it. Your Kelly is beautiful!