Thanks guys.

Getting a bit closer. I re-did the mesh for a much closer end result to what I was thinking. I did manage to get the flow command to work with some extra experimentation and wrapping around half a circle+mirroring the result.

Still some strange issue with edges overlapping, but hopefully I will figure out what is causing the surface alignment issue.

Unwrap of a circle can produce a line of the proper length to use in the input. So either the line or a plane of the lines length is useful.

<< Still some strange issue with edges overlapping

For avoid that make first a single Source first without overlapping itself !