Water will not flow down a flat slide because there is no potential energy difference between the two ends. How could this situation be represented in a electric circuit?

As the water flows according to the difference in potential energy, i.e. it flows from higher potential energy to lower potential energy, the electric current also flows in same way.

Electric current also flows according to the electric potential gradient which is measured in volts. So if two points in an electric circuit have the same electric potential then there will not be any flow of current between the two points. For example, in any circuit, if two points A and B both have a potential of 10 volts. Then there will be no electric current between A and B because the potential difference between between A and B is zero (10 - 10 = 0).