Since ES File Explorer is no longer available for download from Google Play store and the account of the developer allegedly terminated (as on 31st August '19).

We would suggest you to switch to "Wireless File Manager" app to Transfer files to Fire TV. In order to find the app on your TV just say the app's highlighted name on the Voice Remote provided with the TV stick.
Using the app is easy and fairly self explanatory. Still, if you need some help getting started we have detailed how to use the app in our previous post here.

This post is part of the Transfer files to Fire TV series. Following are the steps to follow in order to transfer files from/to your Amazon Fire TV/stick using ES File Explorer.
  1. Install ES File Explorer on your Amazon Fire TV stick. In order to find the app on your TV just say the app's highlighted name on the Voice Remote provided with the TV stick.
  2. Open ES File Explorer on your android device and Amazon Fire TV stick.
  3. Remember, the Fire TV/stick and android/ios/windows device to be connected to the same WiFi network.
  4. Select all the files you wish to send and then tap on send in the options menu and choose your TV stick from the list.
  5. Now choose the location where you wish to copy to and click the OK button in the pop up dialog appearing on the receiving device.