"Ce livre est plat."
"Thin" is not the same as "flat". A book being flat means either that it's boring (figurative kind of flatness) or has no bumps on its cover (unlike many kids' books -- literal kind of flatness). It could be so thin as to appear flat, but that is not a given, and is anyway not a conventional thing to say. Really, it's very unusual to call a book "flat" in anything but the figurative sense.
dull or boring should be the accepted word, not "flat", who would ever say that?
but you just never say that in english. maybe this book is thin (but of all the examples of the word thin, i wouldn't use a book) but flat just sounds wrong. Especially when the word plat has various meanings, many much more normal for describing a book.
a good check to see if a phrase is used in english is google."it is a thin book" has 1.7 million results, "it is a flat book" has just 3, one of which being about the book being flat as in dull, and one other referring to a flat book holder.
Unfortunately, there's just no good word for this that doesn't also have a figurative connotation (eg, "thin", as the discussion below shows and @lemmingofdestiny points out). Even "thick" can be read figuratively to mean "stupid" (just like "dense") -- though these are words more commonly applied to people than books.
As @kmcleann says, you most probably want to just call it short, which it almost certainly is. If however you really want to refer to its physical thickness, you would just have to say a little more to make your meaning clear: "This is a physically thin book".
As a purist I would say you could just use "literally" -- "This is literally a thin book" -- and that's why the word "literally" exists, but sadly, the word "literally" has lost its meaning and is often used in entirely figurative (and non-literal) contexts: you will see even (mediocre) newspapers contain sentences like "He literally vanished" when nothing of the sort is meant.