For static permissions, the easiest way is to modify Engine\Source\Programs\UnrealBuildTool\Android\UEDeployAndroid.cs or the AndroidManifest in the intermediate/android/apk directory. I haven't tried this, but there is also a GUI plugin AndroidManifestConfigurator. If you need runtime permissions, use the Android requestPermissions API.
The default permissions should be fine for the purposes of that doc. Is the app being rejected due to excessive permissions requested?
Ah, cool.
Nah, I am just thinking ahead. Not sure what UE4 does with permissions (especially now that the manifest is being generated on deployment) and that's why I am asking.