The only "Flip" which will affect where the shot hits is that which occurs before the shot leaves the bbl.
The "Flip" which Burrard discussed was not the rise from recoil. It rather was a downard flexing of the muzzles which occured as a result of the inertia of the muzles trying to stay stationary as the gun rose in recoil. This would offset to some extent the recoil rise causing the gun to hit lower than it otherwise would. This flip, flexing or bending of the bbl (Call it what you will) is a different thing than recoil rise.
Recoil rise is quite prevelent in short bbl guns such as handguns. Bore sight a pistol which is properly sighted in & you will invaribly find the bore axis is point "Below" where the shot is going to hit.
Right. BUT that skips over a lot. BUT what really happens is more like this. If you isolate and fix in space the action/bbl breech unit, that unit no longer has a mechanical "up" or "side" reference. If you want to remove the infinitesimal gravity component just point it straight up. When the thing is fired there is no motion in the action unit thing and as a consequence there is no "inertia" in the muzzles resisting rotation to produce some imagined intrinsic flip. What there is is a vibration of some unknown frequency and amplitude generated and the nodes will appear at unpredictable positions since the freq is not known. Pix of vibrating rifle bbls reveal this. Multi-bbl things by virtue of a really complex structure are not gonna vibrate like that and suggesting that there is a single vertical plane of vibration is just absurd. Muzzle displacement, likely in the microns dimensionally, is unpredictable and would vary with different loads altering the amplitude and freq of the vibrations. That's why rifles shoot diff POI w/ dif loads, the vibrational nodes occur at diff places. SO now we have a muzzled displacement that is unpredictable and likely so minuscule as to not exist. And that brings us back to the unfixing of the action in space and mounting a whole gun. NOW the action can rotate and that rotation is dictated a total extent by the geometry of the gun bore axis and that gun/meat interface I mentioned earlier. Now there is an "up" and "side" and force vectors working in each. And that controls the rise of the rise of the gun that 2-piper notes, even while the charge is still in the bbl. And with what he said if you sight in a pistol in a machine rest and then shoot it in hand the poi will radically change, even if you rest the meat on something.
SxS's do not shoot low, they shoot to all kinds of funny places due to the induced vibration in a really complex structure but to so small a distance that measuring it would not be likely. The poi of any gun is totally dependent on the position of whatever sighting apparatus is used and if that is the front bead and your eye then you just gotta get your eye in the right spot. And the magnitude and direction of those recoil vectors goes back to the geometry of the gun/ meat interface.
Tho I've never bothered to measure it, I'd bet vital body parts that all of my guns, O/U's and SxS alike, have no significant difference in the bore axis / eye-bead relationship since they all shot to +/- the same poi. And they all recoil pretty much the same since the stock dimensions are +/- the same as well.
HTH
have a day
Dr.WtS