Here is an old brass barrel with a short flat.
You might also note the low-slung touch hole. This position is lower than the position on Dave B's pistol. The position of the hole needs to be part of your overall planning.
Here are two photos of round fowler barrels. Short flats were filed on some surfaces, but not all the way around. And the one on the right doesn’t have a flat on the left side of the breech.
You do need to give a little thought to how filing a flat into the breech may affect the strength of the breech. As these last photos showed, these fowler barrels had plenty of material in the breech. So we can assume that filing a flat did not weaken the breech in any significant way on these barrels.
If a fellow was using a barrel that didn't have enough material to allow filing a flat, then I supposed he could solder on some material below the mid-line of the barrel if necessary, so as to build up material for a flat. But I have no experience with that.