I'm working on porting SWHX to Linux, it looks like it's almost there, I got the first demo program to run.
Some other longer term possibilities for doing something like Adobe AIR, but open source are:
neash - The "neash" library provides a compatibility layer to allow haXe programs to target both neko and flash9, giving both web browser and stand-alone support. The API follows the flash9 API very closely to allow easy porting from existing code. The neko implementation currently makes use of the NME library, which in turn uses SDL.
announcing neash - A blog post.
xinf - Xinf (Xinf Is Not Flash) strives to provide a unified SVG-oriented API for graphics programming in haXe. Using Xinf, your application can run on Adobe's Flash Player (Version 9 up), our own 'Xinfinity' runtime, and (with limitations) on standards-compliant web browsers like Mozilla Firefox - from the same source code.
