She's our fancy little lady... Nah, that's her beak... she has plenty of things to file her beak on, she just doesn't seem to care about keeping it smooth. Don't know why. I never see her file it on anything, but she has tons of surfaces at her disposal that would work.
I love that bird fluff. It is almost furry, but better
No cause for concern -- it's totally normal. Some birds are more inclined to keep their beaks smooth than others, but flaking or peeling, as long as the shape and color of the beak are normal, and there are no deep grooves or cracks, is fine. Here's an article about it: