If an aircraft were to climb at constant MAP, the reducing atmospheric pressure would cause exhaust back-pressure to decrease. This would make it easier for the gases to flow through the engine. We would have a constant pressure (the MAP) pushing the mixture into the cylinders and a reducing exhaust back-pressure opposing the outflow of exhaust gas. This would increase the mixture volumetric flow rate through the engine.
Perhaps I have a naive mental model of engines but I'm not sure I follow this. The induction and exhaust strokes are different strokes. The gases don't flow through the engine across a MAP to exhaust back-pressure drop. The gas flows into the cylinder during the induction stroke under the pressure from the induction manifold. It flows out of the cylinder during the exhaust stroke against the exhaust back-pressure. Undoubtedly a higher exhaust back pressure means the exhaust stroke soaks up energy from the engine leaving it less power at the crank. But why would that change the volumetric flow rate?