Layout Animation support

ReactNative layout animations are a way to automatically animate when layout changes. Similar to other animation types, LayoutAnimation provides a set of easings (including spring, linear, easInEaseOut).

On Android, certain flags need to be set via UIManager. It's unclear if we'd need to do the same for RNW.

UIManager.setLayoutAnimationEnabledExperimental && UIManager.setLayoutAnimationEnabledExperimental(true);

{...}

changePosition = position => {
  LayoutAnimation.spring();
  this.setState({
    position
  });
};

More info on LayoutAnimation is here: https://facebook.github.io/react-native/docs/layoutanimation

When this work is completed, it should be possible to follow introduction guides like this one: https://blog.usejournal.com/react-native-animations-intro-a71439e07f70

Start with the React Native LayoutAnimation documentation and the UIManager entry point mentioned in the issue, then determine how layout changes are handled in RNW. Done means the LayoutAnimation API works for layout changes on Windows and the linked introduction guides can be followed successfully.