When an external electric field is applied on a weakly conducting liquid, next to each metallic electrode two layers with a net electric charge of opposing polarity appears. These are called heterocharge layers. The electric field exerts a force on these layers. If the electrodes of different polarity have different geometric characteristics a net electric force is produced, creating a net flow. This is the basis of EHD conduction pumping. This technique has a great number of interesting applications, notably in heat exchange devices to be applied in satellites and aerospace systems. Here we consider a flexible EHD conduction pump. An array of symmetric electrodes is deployed on a flexible non-conducting substrate. This flexibility allows the pump to be installed in conduits of complicated geometries, increasing the applicability of the EHD conduction pumping concept. Specifically, we present the results of numerical simulations with a conic flexible pump with several pairs of electrodes. We discuss the structure of the fluid flow and of the heterocharge layers along the pump.