This page contains information on Flash, a proprietary format for delivering audio and video content, primarily over the Internet.
Flash is non-free/proprietary software
Adobe's Flash plugin cannot be included in Fedora because it is not free/libre and open source software. Adobe does release a version of the Flash plugin for Linux, and this can be used in Firefox, Konqueror and other popular Internet browsers. When Adobe releases a newer version of the Linux Flash plugin, it makes packages available for Fedora, but Fedora cannot include Adobe's plugin as long as it is unavailable as free and open source software.
There are other open alternatives to Flash itself, including the patent unencumbered and free WebM, Ogg Theora video and Ogg Vorbis audio formats. Fedora has complete support for such open formats, and Fedora includes several web browsers including Firefox, Epiphany etc that plays Ogg and WebM files directly, without any need of third party and proprietary browser plugins.
YouTube and WebM support
Google has open sourced an implementation of VP8 video format and combined it with Ogg Vorbis audio and an adaptation of the Matroska container, creating a new format for free and open video and audio called WebM. YouTube is switching over to using WebM extensively and Fedora has embraced this format as well. Current versions of Fedora support WebM by default.
To enable support for it in YouTube, go to http://youtube.com/html5 and click on "Join the HTML5 Beta" link in the bottom of that page. Note that all videos are not available in WebM format yet especially videos that include advertisements but majority of them should play just fine.
For information on installing the plugin, refer to Ask Fedora Flash page