Adding sketches in flat pattern is not very stable from my experiences. But I observe it's getting better and better from NX version to NX version.
I believe in your example (sorry, a screenshot does not tell everything) not the shape is the issue, but the sketch. We do (or try) to do use Flat Pattern of Sketches, but seen issues e.g. when a sketch line is directly on a tangent line, when sketch lines are interfering each other etc.
I made a small test with a Lofted Flange between two half circles (sheet is conical) and a 3D line on Surface, the line is visible in the Flat Pattern. So maybe - it's not the shape.
I don't understand, if it's intended to FP the circles - which look they are closed outside the solid and also then outside of the FP.
Just try step by step and with try and error to add single curves.
What us helps (but we "only" use sketches on flat tabs/webs) is to do small thickness changes with Extrudes, in your case e.g. for the Texts. It's not nice, but it works.
Another thing you can do is: Instead of the FP with sketches do a Flat Solid, you "paint" your sketches on the FS and do a FP with additional curvers from the FS.
