Amazon Instant Video and other DRM-laden flash websites don't work out of the box with flash on Fedora 19. Below is the list of steps I took to get this working in case it helps anyone else. The majority of these instructions were pieced together from the post and comments at http://wtogami.blogspot.com/2012/12/amazon-instant-video-on-fedora-16.html. The linked RPMs were originally taken from that post and recompiled for Fedora 19. These steps have only been tested in Firefox and 64 bit Fedora 19 - I don't think they'll work for Chrome.

First, head to http://get.adobe.com/flashplayer/ and download the "YUM for Linux (YUM)" RPM. Then:

# Install Adobe Flash and its browser plugin
sudo yum install -y adobe-release-x86_64-1.0-1.noarch.rpm
sudo yum install -y flash-plugin

# Install a simple SELinux policy file for Flash
sudo yum install -y policycoreutils-devel
wget http://togami.com/~warren/archive/2012/adobedrm.te
checkmodule -M -m -o adobedrm.mod adobedrm.te
sudo semodule_package -o adobedrm.pp -m adobedrm.mod

Download the fakehal RPMs for Fedora 19 at http://thinkingconcurrently.com/files/f19_flash/fakehal-0.5.14-7.fc19.x86_64.rpm and http://thinkingconcurrently.com/files/f19_flash/fakehal-libs-0.5.14-7.fc19.x86_64.rpm

# Install the fakehal RPMs
sudo yum install -y fakehal-0.5.14-7.fc19.x86_64.rpm \
  fakehal-libs-0.5.14-7.fc19.x86_64.rpm

At this point, make sure all Firefox windows are closed.

rm -rf ~/.adobe/Flash_Player/
sudo mkdir -p /usr/share/hal/fdi/preprobe \
  /usr/share/hal/fdi/information \
  /usr/share/hal/fdi/policy/20thirdparty \
  /var/cache/hald/
sudo ln -s /usr/share/hal /etc/hal
sudo touch /var/cache/hald/fdi-cache
sudo systemctl start haldaemon.service

Now start up Firefox and watch your favorite Amazon Instant Video. Let me know if it works for you!