Can you paste a copy of your Appium logs? You can paste a copy of your logs with Github Gist or Pastebin.
Can you also post the Android API level of your device? Connect your TV with adb, and then run
adb shell getprop ro.build.version.sdk. Uiautomator should be available for devices running API 17 and newer; older devices have to fall back to using Selendroid.
It's also possible that Amazon might have heavily altered their version of Android and stripped out Uiautomator. I hope they don't do that, though, because that's just a waste of resources for no practical benefit.