Hi Heiner - thanks for including the object. That may be a bit difficult to get a good result due to some of the tight bends in your target shape, but here's how you would control it:

First, it's best if the base surface is a simple plane, rather than a surface that just happens to be flat but has some internal warping to it as will happen if you have done a network or a loft between various bent curves. It seems that you have the latter type of surface as your base plane currently, this is probably the source of much of your problems. Here I've drawn in a base plane (the blue one) using Draw solid > Plane > 3 pts:



If you load the attached 3DM file and select the blue plane in it and then turn on its control points using Edit > Show pts, you'll see it is a very simple structure with just 4 control points at the corners. If you do the same to your base plane you should see that it's much more complex with a lot of points it making up, and the surface is kind of internally bent at the corner areas - bending laterally I mean even though it is all flat. The layout of the base plane's control point grid will have a big impact on how Flow works so it's not good to have that kind of surface as your base surface.

Once you have a basic plane as your base surface it will probably help you out a lot - because it's all bent internally it's not so easy to know where the corners of your surface were actually at. With the simple 4 point plane it's a lot easier to know where the 4 corners of the actual surface are located at.

Then to do the Flow, select your object to be deformed (and have only it selected, don't have the base plane or target surface selected yet) then run Transform > Deform > Flow. At the first prompt that says to select the base curve or surface, click on the blue plane and make sure to click on it in one of these 8 point zones, each of which are along an edge towards one side of the edge, but not right at the corner:



You can click on whichever of these 8 points is most convenient, for example I'd suggest clicking on the upper right one like right here:




Then at the next prompt to click on the target surface, there are again 8 zones on the target surface that you want to click on - you will be controlling how the 2 surfaces map to one another by this association. So for this example since we clicked on the upper right one, you want to click on the upper right zone of the target surface, meaning in this location here:




That will be telling Flow to match the top right of the base plane to the top right of the target surface. That will produce this kind of result here:



If that's the wrong side of the surface then there is an additional control on the final Flow stage that you can enable to correct that, that's the "Flip surface normal" checkbox here, when activated it will flip the flow result to the opposite side of the surface normal direction:




I hope that helps to clarify how you'd control Flow for this particular case.

One other note - depending on how the target surface is constructed it can be possible for the result to be sensitive to the control point spacing of the target surface, like if the surface was constructed from an extrusion and the control points in the curve that was extruded had some different spacing along the curve the flow result can stretch or squish along with those changes in spacing. You can help to reduce this by running the Rebuild command on the curve before extruding it, or using the "Refit" option in Loft if you're generating it with Loft.

- Michael