Hi Brian & Gunter, to use Flow you'll need to build a flat surface through these curves but you need to use either sweep or network to do it so the "underlying surface" has its UV structure going in that direction. Don't use Construct > Planar for this case because that will make a large 4 point plane that's trimmed, and Flow will use the structure of the underlying surface to do its work:


If you turn on the surface's control points it should look like this with the control points hugging the curve contours, if you make it using Construct > Planar and turn on those control points you'll see it looks different with there being a large plane made up of just 4 corner points with the curves being trim curves rather than being part of the underlying surface's structure:



Also you'll probably need to cut that in half since your cone surfaces are cut in halves too.

- Michael