I'd like to point out that tidy with respect to having things in order is a nearly exclusively British word. We Americans use untidy (although not often) in the sense of messy, but the Keep Britain Tidy signs around the UK roads are Keep America Clean signs in the US. Americans will say clean and tidy to add emphasis to the word "clean," but very rarely use "tidy" on its own in this way. Of course, since you are saying "flat" instead of "apartment," it would seem that you are looking for British English, but I thought it might be useful to mention this.
I believe I understand what you are looking for. My father, a law professor and writer, had in his office a folding banquet table of the sort that would seat 12, always covered entirely with at least a hundred books. Some would be opened to a particular place and placed on their faces in lieu of a bookmark, with others similarly opened and stacked on top of them. You are looking for a word to describe this sort of situation.
A French friend of mine once referred to her children's playroom with the wonderful le bazaar, but we don't have anything that captures the idea quite so colorfully. Disorganized is a neutral word, simply meaning not organized. If you want to avoid the idea of dirty, you could use, to add a few to the suggestions already given, haphazard, disorderly, or the understated unsystematic. The latter can convey a rather humorous attempt to be polite: "'The flat was organized in a way that might be described as ... unsystematic,' he said, sardonically raising an eyebrow."