Wouldn’t the flow get bigger as the river flows towards the mouth? Ie, the biggest flow is typically where it ends, not closer to the source.
The overal water volume would but not the flow; water flow & velocity is decreased by friction along the river bed, so it is slowest at the bottom and river banks/edges - and the further it gets from the river source, i.e. Cowichan Lk - and fastest near the surface and in the middle. The velocity below the surface is typically slightly higher than right at the surface because of friction between the water and the air. More volume results closer to the estuary because the river bed/basin gradually widens and flattens as it approaches the bay allowing for that increased volume. Further up the river are where the deeper sections and pools are, Sandy Pool being one of those. Less volume - but more flow as the river is squeezed into those deeper and narrower sections which also decrease in elevation frrom the source more sharply than does the river further down as it gets closer to the bay. Hence the river becomes more "lazy" than further up towards Riverbottom for example.