Thanks for posting the file. So yes I'd think your best bet would be using Flow, but your base surface there isn't just a simple full surface it's a trimmed surface and Flow only works on a full surface and will ignore the trim. So it's probably best to untrim it and then work on trimming the results later. If you had a cutting surface that you used to trim your surface maybe it would work for cutting both pieces.

So to make the variable offset in the attached file, I prepared 2 planes off to the side and used control point editing to move one point upwards. Then I untrimmed your surface (select all boundary edges and hit delete), then selected the edited plane, ran Transform > Deform > Flow and used the plane underneath as the base surface and your twisty surface as the target surface.

- Michael