The Mac OS/X is a similar architecture to Linux (since both are based on the Unix style), but it is different enough to make it non-trivial to port an application from one to the other.
There are several ways to run flash in Linux - using the non-free Adobe browser plugin, and using open source applications such as gnash or swfdec. Some of the video applications will play flash video. This assumes that your flash project is an swf or flv file.
If you want to create/use a standalone flash projector, you will need to look at the "Linux Debugger and Standalone Players for Flash Developers" download available from the Adobe website
But being able to create such a projector automatically from Creative Suite? This is something you would take up with Adobe directly. It would not be easy, because there are significant differences between Linux distributions, kernels, and the range of processors that Linux runs on. A single binary executable could not work on everything.