Commentary for Avodah Zarah 144:4

If flow contaminates the upper liquid, then the wine in the container should also be nesekh. The Talmud has to therefore say that the baraita refers to a case where he cuts off the flow from the top to the bottom before it reaches the bottom container. This would seem to be a recipe for mess.

The second clause in the mishnah says that the wine in the bottom vessel is prohibited. We could deduce that what is in between is permitted, leading to the conclusion that flow is not a connecting link.
In the end, nothing can be learned from this mishnah concerning the concept of flow. [I might add that clearly the simple reading of the mishnah is that downward flow is not a connecting link. The Talmud does not seem to want to prove this quite yet].