Adobe's Flash Player 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. The Linux plugin is only available for x86 architectures. If and when Adobe releases a newer version of the Linux Flash plugin, packages will likely become available for Fedora, but Fedora will be unable to include Adobe's plugin as long as it is unavailable as free and open source software.
If you must use Adobe's Flash plugin, consider using the packages provided by mplug.org. Fedora does not endorse or support these packages, but they provide a much cleaner installation on Fedora systems and may include corrections over Adobe's installer that will allow them to operate correctly on Fedora systems.
For more information about Fedora's policies against proprietary software and formats, see our ForbiddenItems page.