I checked with my friend EJ, the most knowledgeable person on these matters that I know, and this is what he wrote back:
"The confusion seems to come from the fact that most gun flaps today aren't really properly cut. The flap is essentially a "capelet", designed to button over and keep water from running into the upper corner on the buttoned side of the coat. If you button up a trench coat, you may notice that the part just infront of the collarbone is just one piece of fabric on top of the other, and the overlap is open on the top edge. This lets water in, and if you raise yr arms (for any reason, but for example, shouldering a rifle), it has a tendency to open up even more by separating the lower and overlapping side of the coat. The gun flap covers it. It all seems vy arcane and fussy (which it is), but it's also vy Victorian.
This rather stylised example shows on used more-or-less properly:http://www.kitmeout.com/img_assets/burberry1_blog.jpg