D.Taylor...
When I cut a button hole in leather, I punch a round hole where the base of the button and thread attachment will be, and cut a slit toward the base end just large enough so the button will pass with relative ease.
Yup. Works best on a bag, but don't get too persnickety about..."proper"...unless you are trying to duplicate a particular historical piece.
I've also found that, when mounting buttons without a stem, it helps the function if you wrap the thread around itself just under the flat button of the button. A couple of wraps before sending the needle through the leather for the last time raises it just enough to compensate for the thickness of the flap that will secure to it.