So ever since I got Chromecast I was able to watch TV shows/Movies/etc... through Amazon Prime Movies. I was able to do this on my downstairs computer with no problem. With my upstairs TV I wasn't able to cast it. Well, on my upstairs TV I notice that it told me that I need to install Microsoft Silverlight (when I clicked on a show/movie to watch, it tells me to install Silverlight). Well I installed it and hit my cast button on my Google Chrome Browser, and it gave me nothing on my Google Chromecast only a blank screen.
So I uninstalled Silverlight, because if my downstairs computer is able to cast Amazon Prime Movies on my Google Chrome, there has to be a way for my upstairs TV to do so, and I was going to get it to work. So, I went to try to watch a show again. I clicked the "watch now" icon on the site to watch the show. I notice in then lower right hand corner, below where it tell's me to install Silverlight it says "Or watch it through Adobe Flash." So, I hit that (the Adobe Flash one) and it finally broadcasted just fine on my Google Chromecast, when I hit the cast button on my Google Chrome Browser, and I was able to get Amazon Prime Movies on my Chromecast.
So, in case you guys are having trouble watching Amazon Prime Movies on Chromecast try doing what I did. You might need to uninstall Microsoft Silverlight though.
To uninstall Silverlight I had to go this link (below) to get the directions (I will try to do it the normal way first Control Panel- Add/Remove programs-Uninstall), I couldn't do it the normal way for some reason.
Updates to Silverlight won't install and can't uninstall - Microsoft Community