Oh yes, this is an experience that many rabbit-owners have to deal with.
Some bunnies aren’t good at cleaning their bums. I have one of those. He’s not fat and I doubt he’s arthritic, but both over-weight and athritis may stop a bunny from cleaning her/his butt. The little squeak she makes may mean she feels some pain in her back when she tries to clean herself. It’s most common in elderly bunnies, of course.
The general advice is to feed more hay, since hay is low calory/high fiber. Oftentimes the sticky butt is due to excess cecals, the “poop” the rabbit is supposed to ingest. If to much of that is produced, it may be the result of a too rich diet.
Getting rid of the flaky skin may help too, since fur mites (I suspect fur mites as the reason for the flakiness) obviously are a challenge to the immune-system, and getting that problem sorted will be beneficial for her general health and well-being. And on the off chance that the sticky poop has some sort of parasitic reason, the med for the mites will deal with internal parasites as well.