The effect of this is that the Ocean at the equator is 20km further from the centre of the Earth than at the poles. The shape of the Earth is, to first approximation a slightly flattened sphere. Rivers do not creep towards the equator by centrifugal force because the rocks and the oceans already did so millenia ago and made a hill that exactly balances the centrifugal force.
Rivers flow downhill.
Whichever way is down, there they go. The Amazon is a great example that beats your theory. It is near the equator and flows from the Andes in the west to the Atlantic in the east. Locally, rivers can get trapped in mountain belts and have to flow parallel to them before they can get round the end. Look at the Ganges and the Brahmaputra that have to flow around the Himalayas.