Hi there and welcome
You cannot do this via the browser on the TV, what you are seeing is for the computer, to use this browser. The browser on the TV is very limited and cannot run the plugins needed for this.
What you need to do to use Amazon Prime is the Amazon Fire Stick
You can get it here
CLICK ME TO OPEN
You connect it to a HDMI port on the TV and you can then stream prime and a host of other apps via the stick
If you would like any additional information or assistance, please do not hesitate to let me know.
Else if you can take a second to rate my service by clicking one of the stars at the top of the screen then submit, that would be greatly appreciated.