the Haxe user has been here for a long time, although I personally mainly use Haxe for web application projects, not NME. Until recently, the main activity of the NME was (far and far) the game. Recently, attempts have been made to create good tools for creating user interfaces based on the strengths of the NME platform:
https://github.com/RealyUniqueName/StablexUI - Demo (works on HTML5, flash, native desktop and mobile)
https://github.com/ianharrigan/haxeui
but they are very fresh additions, so if you are looking for a tried and tested Kivy solution (never heard of this before, but it looks cool!) it looks like he has a bit more maturity and a little more benefit for him.
In terms of performance and overall reliability, Haxe / NME is great, but getting these user interface widgets with their own feel will be your painful point. Other than that, it's a terrific language to work with :) Python is very good, though ... each in its own way!
At the time of writing, people were experimenting using their own user interface (the objective of Objective C is discussed at the upcoming conference, and the goals of Java and C # are becoming more mature, so there are 3 main mobile platforms), so this may be an option if you want to use ui's own components, although it is not ready yet, I just hope it can become a reality within the next year or so :)
Good luck with your project anyway! If you decide to go with Haxe / NME, be sure to ask questions (or here, NME forums or the Haxe mailing list) so that people can help you on your journey.
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