This part of FAR 23.1447
(c) If certification for operation above 18,000 feet (MSL) is requested, each oxygen dispensing unit must cover the nose and mouth of the user.
Ian

Nasal cannulae will always have outside air entrained into the inspiratory stream, diluting the oxygen. A very high flow rate would help this, but >4-5 l/m becomes very uncomfortable and uses oxygen supply quickly. Nasal reservoir bags work to some degree, but without a gas tight fit in the nare, it is not as efficient as a well fitted mask with bag. A beard dramatically reduces the efficiency of a mask for the same reason.
4 liters O2 by nasal cannula at 18,000' will result in a sea level equivalent of approx 25% oxygen, 2 liters, about 18%. The 18,000' is arbitrary, but coincides with FAA Class A airspace and is a reasonable estimate of where a cannula is unable to reasonably provide the normal 20% (sea level equivalent) O2.
An on-demand system with cannula, such as Mountain High, is superior at higher altitudes. Flow occurs only on inspiration, reducing drying, usage, also, the oxygen delivered comes early in the I/E cycle, and most of it reaches gas exchanging portions of the lung.
P

The assembled wisdom seems to be that IO's comment that as long as your O2 saturation is ok (say above 90) that is all that is necessary to be safe - even if you are achieving this using a cannula (or a pipe 'up your back orifice') or some other method. (obviously not legal in FAA land)