First install the Flash plugin from the negativo17 repository. Execute the following commands as root:
yum -y install flash-plugin
setsebool -P unconfined_mozilla_plugin_transition=off
Basically this will make the flash plugin work already. You will have to restart your browser.
For Amazon Instant Video however, you also need to install this additional package in order to enjoy your movies on Fedora:
yum install http://downloads.sourceforge.net/project/postinstaller/fedora/releases/22/x86_64/libhal1-flash-0.3.0-1.20150415git2b27363.fc22.x86_64.rpm
Finally go to this link and change the default playback plugin from Silverlight – which is the default – to flash.