The term "flat website" can have negative connotations and can be misinterpreted as a negative thing; perhaps conjuring the image of a site which only has a handful of pages, or in other words the opposite of a content site.
This is less an architecture and more of a mini site - a site which is made up of just a few pages.
These kinds of sites do not rank well because Google loves content and if your site is only made up of a few pages, it may get the idea that you do not provide very much value to your readers or worse your site exists solely for the purpose of selling or capturing leads.
The reality is that a flat website is actually exactly what you want from your site as this refers to the architecture of your site and how user and search engine friendly it is.
As a webmaster, you want to develop your site into a content site as this significantly helps you in the search engine results pages.
You want to be careful with how you organize your site, however.
You never want to and should never have a reason to go beyond 3 levels.
The lower your content is located in terms of levels, this makes it increasingly difficult for search engines to crawl.
If it's too difficult for a search crawl spider to find your content because it's buried 5 levels down, it won't find it and it won't index it; so that can result in your having potentially dozens if not hundreds of pages of good content which no one will ever see unless they navigate to them from on your website itself.
In the same vein, the more levels you have, the more difficult it is to spread link juice amongst your pages; so you're effectively shooting yourself in the foot as far as ranking in the search engines is concerned by using too many levels for your content.
Note that there are too many levels of content, it's difficult to access many of the deeper levels without having to go through this linear path first, and ultimately it's too confusing and complex for both the search engine crawlers and anyone browsing your site.
It may seem like sites with levels of 5, 6 and beyond are easier for organizational purposes, but it's not helping you with your readers or the search engines.