Is there a standalone Flash Player for Linux?

I suggest you try Adobe's "Linux debugger and standalone players" package (TGZ) which can be found at Adobe Flash Player - Downloads. Excerpt:

2/11/2010 Updated Linux debugger versions (aka debug players or content debuggers) of Flash Player 9 are now available. Additionally, the Linux standalone player (projector) is available for developers who wish to publish projectors on Linux operating systems [my emphasis]

Edit: The newer version of this can be found here - you can download & extract this, and run it by opening the flashplayerdebugger file.

Try Gnash: http://www.gnu.org/software/gnash/

Try CrutziPlayer: http://www.crutzi.info/crutziplayer

It executes the flash plugin, but uses xcomposite, xfixes and cairo to scale the output from native swf resolution to fullscreen.