The problem is one of parametrization of your surface - it’s a difficult concept to understand. NURBS surfaces are not necessary linear in their parametrization. What that means is if you traveled along the surface from end to end, instead of going at a constant speed everywhere, you will go faster in some places and slower in others. The places where you go faster, the objects being flowed will be ‘stretched’, and where you go slower, they will be ‘compressed’
There are two ways to approach this. One is to try to create a surface with a more even parametrization for your flow target. That is possible by rebuilding the edge curve with a lot of points and then making a new target surface from that.
However, the easiest is to try to duplicate the parametrization of the ‘to’ surface in the ‘from’ surface. You can easily do this in your case by using UnrollSrfUV on your original.
In th file below, I ran UnrollSrfUV, then rotated the result by 90 and moved it near the other. See how the surface isocurves on the unrolled surface match those your curved surface? I then copied your pattern onto the surface. I also needed to use Dir and SwapUV to get the directions right (you need to experiment with this a bit)
Then I used FlowAlongSrf and clicked near the * which correspond on the from and to surfaces (make sure you have AutoAdjust=No set in the FlowAlongSrf options).
FlowUV.3dm (1.1 MB)