Depending on the model of your Fire tablet, you may or may not be able to share the screen to compatible TVs. Certain older models of the Fire tablets have an HDMI port which you can use to connect to a TV. However, this was discontinued several years ago and the new models don't have this option.
The best solution if you want to watch stuff from Amazon Video (as I interpreted the title of this post to mean) is to get a Fire TV Stick. They are fairly inexpensive ($50 for the newly released ones as of the time of this post - you can still find old generations for less.)
Also, if your Vizio is a smart TV, then it likely has the Prime Video app available for it. With that app you can just sign into your Amazon Account and access Prime...