A demonstration of the proper key placement (at the top of your widget tree) in scenarios that require keys.

fixed.dart

void main() => runApp(new MaterialApp(home: PositionedTiles()));

class PositionedTiles extends StatefulWidget {
  @override
  State<StatefulWidget> createState() => PositionedTilesState();
}

class PositionedTilesState extends State<PositionedTiles> {
  List<Widget> tiles = [
    Padding(
      // Place the keys at the *top* of the tree of the items in the collection.
      key: UniqueKey(), 
      padding: const EdgeInsets.all(8.0),
      child: StatefulColorfulTile(),
    ),
    Padding(
      key: UniqueKey(),
      padding: const EdgeInsets.all(8.0),
      child: StatefulColorfulTile(),
    ),
  ];

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Row(children: tiles),
      floatingActionButton: FloatingActionButton(
          child: Icon(Icons.sentiment_very_satisfied), onPressed: swapTiles),
    );
  }

  swapTiles() {
    setState(() {
      tiles.insert(1, tiles.removeAt(0));
    });
  }
}

class StatefulColorfulTile extends StatefulWidget {
  StatefulColorfulTile({Key key}) : super(key: key);
 
  @override
  ColorfulTileState createState() => ColorfulTileState();
}

class ColorfulTileState extends State<ColorfulTile> {
  Color myColor;

  @override
  void initState() {
    super.initState();
    myColor = UniqueColorGenerator.getColor();
  }

  @override
  Widget build(BuildContext context) {
    return Container(
        color: myColor,
        child: Padding(
          padding: EdgeInsets.all(70.0),
        ));
  }
}

If anyone is following Emily's tutorial https://medium.com/flutter/keys-what-are-they-good-for-13cb51742e7d
Here's the final main.dart file
change the dart import 'package:flutter_web/material.dart'; to import 'package:flutter/material.dart'; if your on the modbile

import 'dart:math';
import 'package:flutter_web/material.dart';

void main() => runApp(new MaterialApp(home: PositionedTiles()));

class UniqueColorGenerator {
  static List colorOptions = [
    Colors.blue,
    Colors.red,
    Colors.green,
    Colors.yellow,
    Colors.purple,
    Colors.orange,
    Colors.indigo,
    Colors.amber,
    Colors.black,
  ];
  static Random random = new Random();
  static Color getColor() {
    if (colorOptions.length > 0) {
      return colorOptions.removeAt(random.nextInt(colorOptions.length));
    } else {
      return Color.fromARGB(random.nextInt(256), random.nextInt(256),
          random.nextInt(256), random.nextInt(256));
    }
  }
}

class PositionedTiles extends StatefulWidget {
  @override
  State<StatefulWidget> createState() => PositionedTilesState();
}

class PositionedTilesState extends State<PositionedTiles> {
  // Stateful tiles now wrapped in padding (a stateless widget) to increase height
  // of widget tree and show why keys are needed at the Padding level.
  List<Widget> tiles = [
    Padding(
      padding: const EdgeInsets.all(8.0),
      key: UniqueKey(),
      child: StatefulColorfulTile(),
    ),
    Padding(
      padding: const EdgeInsets.all(8.0),
      key: UniqueKey(),
      child: StatefulColorfulTile(),
    ),
  ];

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Row(children: tiles),
      floatingActionButton: FloatingActionButton(
          child: Icon(Icons.sentiment_very_satisfied), onPressed: swapTiles),
    );
  }

  swapTiles() {
    setState(() {
      tiles.insert(1, tiles.removeAt(0));
    });
  }
}

class StatefulColorfulTile extends StatefulWidget {
  StatefulColorfulTile({Key key}) : super(key: key);

  @override
  _ColorfulTileState createState() => _ColorfulTileState();
}

class _ColorfulTileState extends State<StatefulColorfulTile> {
  Color myColor;

  @override
  void initState() {
    super.initState();
    myColor = UniqueColorGenerator.getColor();
  }

  @override
  Widget build(BuildContext context) {
    return Container(
        color: myColor,
        child: Padding(
          padding: EdgeInsets.all(70.0),
        ));
  }
}