Don't think there is an actual oil flow requirement for piston rings. The piston skirts need oil, but the rings only need to stop oil from getting to the combustion chamber. The amount of oil they need to prevent metal to metal contact is minimal and the oil they get is thrown off the main and rod bearings.
There are, however, calculation methods to estimate the oil required by hydrodynamic bearings (mains, rods, cam, other bushings). Piston spray jets could be included. The total pump flow is always more than the engine needs in order to build up pressure, so there is plenty of oil left over for splash lubrication of cylinders, lifters, etc.