Read the documentation here http://facebook.github.io/react-native/docs/animated.html#flattenoffset.

flattenOffset, like setOffset, is grouped with other Animated.ValueXY methods because it is going to typically be used when dealing with PanResponder, and called in the onPanResponderRelease function.

flattenOffset will take whatever values are in the offset and add them to the base animated value, and then reset the offset to 0. For example, if we had an offset of 100 and our Animated.Value is 50, when we call flattenOffset, our offset will become 0 and our Animated.Value will become 150.

  componentWillMount: function() {
    this._animatedValue = new Animated.ValueXY()
    this._value = {x: 0, y: 0}
    this._animatedValue.addListener((value) => this._value = value);
	this._panResponder = PanResponder.create({
      onMoveShouldSetResponderCapture: () => true, //Tell iOS that we are allowing the movement
      onMoveShouldSetPanResponderCapture: () => true, // Same here, tell iOS that we allow dragging
      onPanResponderGrant: (e, gestureState) => {
        this._animatedValue.setOffset({x: this._value.x, y: this._value.y});
		this._animatedValue.setValue({x: 0, y: 0});
      onPanResponderMove: Animated.event([
        null, {dx: this._animatedValue.x, dy: this._animatedValue.y}
      ]), // Creates a function to handle the movement and set offsets
      onPanResponderRelease: () => {
        this._animatedValue.flattenOffset(); // Flatten the offset so it resets the default positioning

// To use

<Animated.View style={[styles.box, {transform: this._animatedValue.getTranslateTransform()}]} {...this._panResponder.panHandlers} />

In this context, flattenOffset is taking what ever is set in the offset and merging it in with the animated value. We use flattenOffset to reset our offset back to x: 0, y: 0. Because we reset our offset and our animated value in the onPanResponderGrant, the call to flattenOffset is unnecessary, here. However, in the case where we want to trigger an animation from the released location to another location, flattenOffset is required.