From Fedora Project Wiki

Flash on Fedora 10

Suitable flash plugins (players) should be installed for playing flash content in web pages. Fedora provides the open source players Gnash and Swfdec. Both these players are under heavy development. As of now, Gnash can deal with about 81% of the open Flash specifications. Most of YouTube files can be played on Gnash. For more details see the [Gnash manual]. "Swfdec" is also efficient on many flash files.

The proprietary flash plugins provided by Adobe do not ship by default in Fedora 10. Users intending to use the proprietary flash players provided by Adobe may note that Flash Version 9 is NOT Supported. But Flash 10 is known to work in both the X86 and X86_64 architectures (with some hiccups).

X86_64 users need to install all of flash-plugin, nspluginwraper.X86_64 and alsa-plugins-pulseaudio.i386 for the 32-bit flash player. The last of these must be changed for the 64-bit alpha version.

X86 users need to install all of flash-plugin, nspluginwrapper.i386 and alsa-plugins-pulseaudio.i386' from adobe's yum repository. For SELinux related problems see this.

Note this that no flash player can be expected to play all flash files, and in any operating system.