I don’t know, I can never figure out how to use FlowAlongSrf without first being given an explicit solution. Maybe it’s me, maybe the tool is unintuitive, I don’t know…
flow-problem.3dm (192.9 KB)
Why does the above result not wrap to the actual surface?
you need to create a single surfaces as base / target.
and as you use a circular target surface - use unrollSrfUV…
EDIT:
ok i hope this is what you re after
flow-problem_tp_rh7.3dm (177.2 KB)
the workflow I did:
_dupEdge
_join
(useExtrusions = no, CreaseSplitting = Disable)
_extrudeCrv (split at Tangents = no)
_dot to identify orientation in 2d
… result is a single surface, not a polysurface
_unrollSrfUV (you get a base surface with same structure as 3d - important because of circular part)
I never use the autojust option in flowAlongSrf
I always check UV with _Dir and pick corresponding points. -the dot s will help to do this
Great… I always forget that so few commands work with polysurfaces in Rhino, and that Rhino almost never warn about this. And the situation is similar with rational surfaces… here’s the result of MergeSrf in my example when I tried to convert it to a single surface… 
… I would recommend not to use trimmed surfaces as target.
_explode
_untrimAll
_mergeSrf (smooth = No)
will also give do the job.
_dots … _unrollSrfUV … see above
(see Edit of my initial answer)
Yes, thanks. I keep forgetting that in addition to not helping with polysurfaces and rational surfaces, Rhino also doesn’t help you with trimmed surfaces (like automatic shrinking before MergeSrf). It really is like a hand saw, when you’re used to other CAD software which are more like power tools. 
But I also noticed that UnrollSrf gives a “sort of” ok result, but not really good, while UnrollSrfUV gives the actual good result… but luckily, I didn’t have to identify orientations or check directions like you suggested, because since I roughly placed the curves where I wanted them in 3D, both unroll commands copy the curves to the unrolled 2D surface, which is a nice help.
The question now is, how do I remember to use UnrollSrfUV and not UnrollSrf the next time I want to do something similar? 
It’s funny how some plug-in developers can do more professional looking software than McNeel themselves… 
Anyway, the hardware dongle requirement is just silly, so nice to see but not for me.
There are other tools that work professionally and are very powerful. You can watch videos on the site.
Maybe on purpose. They do not want to compete with third-party tools
How to get this plugin
