Originally, there were specific rules about coats and whether they were supposed to have jetted pockets or flap pockets. On the one hand, all formal garments had jetted pockets, including coats with peaked lapels. That’s why you should never see any welt pockets on a tuxedo or a Stroller or Stresemann.
On the other hand, informal coats were equipped with flap pockets. This was quite practical because the flap prevented things inside the pocket from falling out. All country suits and coats with notched lapels were considered to be informal. However, if a coat had patch pockets, it sometimes did not have flaps. In that case, the patch pocket often had a button as well as a buttonhole on the inside in order to achieve the same loss-preventing effect of a flap.
Today, the distinction between formal and informal coats and subsequently the decision for one kind of pocket over another is mostly obsolete. This is probably due in part to the fact that many suits and coats have notched lapels today. Another reason is surely the flap itself which is sewn on in a way so it can be tucked into the pocket. As I mentioned before, the tuxedo is one of the very few garments left that still does not have flaps—simply jetted pockets. In my opinion, it is a nice detail to to have the jetted pocket made out of silk or satin, depending on what you used for your lapels.
The next time you are wearing a coat with peaked lapels, try to tuck the flaps in and ask yourself whether it looks more elegant that way—chances are it will.