Thanks for the quick reply! I didn't even think about that, but it makes sense: those stitches could probably do some painful damage to bare skin, especially if one properly cuts as opposed to just hits with the thing.
Chris is undoubtedly correct but we always did the opposite, which I guess makes us incorrect...
I was taught to glue the flap on the lacing side down with hide glue. We also forced some glue into the folds of the tip to ensure that the knotted end didn't turn inside out, which happens some times if you don't. Although the leather on our shinai is rough out, we use shellac to smooth it out. I use spray shellac, giving it multiple coatings. Letting each dry and sanding it smoother each time before the next coat. Eventually it gets very smooth. use will polish it even further. This process makes the flap / lacing side virtually flat so the issue of it being more abrasive to the partner is moot at that point.