Hi,
Flux implies that something is moving, real or possibly not real.
A field is nothing more than a region where we can assign at least one value to every point in the space of that field. So if we had a closed stainless steel cube filled completely with water (the water with some dissolved oxygen) under some pressure we could describe every point inside that cube as having a certain constant pressure. And as we strike the cube on one side with a hammer there would be created a pressure wave starting from that one side to the other (at least) and that would mean we would have to assign higher values to points on the side that was struck at least during the first moments of impact.