Código relacionado con el post "WebAuthenticationBroker y métodos AndContinue | C#" http://juank.io/windows-phone-webauthenticationbroker-metodos-andcontinue/

App.xaml.cs

//Code to add into app.xaml.cs
//this file must be previously generated by Visual Studio 2013 templated project


ContinuationManager _myContinuationManager = new ContinuationManager();

protected async override void OnActivated(IActivatedEventArgs args)
{
    CreateRootFrame();

    if (args.PreviousExecutionState == ApplicationExecutionState.Terminated)
    {
        try
        {
            await SuspensionManager.RestoreAsync();
        }
        catch { }
    }

    if (args is IContinuationActivatedEventArgs)
        _myContinuationManager.ContinueWith(args);

    Window.Current.Activate();
}

private void CreateRootFrame()
{
    Frame rootFrame = Window.Current.Content as Frame;
    if (rootFrame == null)
    {
        rootFrame = new Frame();
        SuspensionManager.RegisterFrame(rootFrame, "AppFrame");
        Window.Current.Content = rootFrame;
    }
}

BasicPageFB.xaml

<Page
    x:Class="WABAndContinueDemo.BasicPageFB"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:local="using:WABAndContinueDemo"
    xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
    mc:Ignorable="d"
    Background="{ThemeResource ApplicationPageBackgroundThemeBrush}">

    <Grid x:Name="LayoutRoot">

        <Grid.ChildrenTransitions>
            <TransitionCollection>
                <EntranceThemeTransition/>
            </TransitionCollection>
        </Grid.ChildrenTransitions>

        <Grid.RowDefinitions>
            <RowDefinition Height="Auto"/>
            <RowDefinition Height="*"/>
        </Grid.RowDefinitions>

        <!-- Title Panel -->
        <StackPanel Grid.Row="0" Margin="19,0,0,0">
            <TextBlock Text="Demo WebAuthenticationBroker" Style="{ThemeResource TitleTextBlockStyle}" Margin="0,12,0,0"/>
            <TextBlock Text="AndContinue" Margin="0,-6.5,0,26.5" Style="{ThemeResource HeaderTextBlockStyle}" CharacterSpacing="{ThemeResource PivotHeaderItemCharacterSpacing}"/>
        </StackPanel>

        <!--TODO: Content should be placed within the following grid-->
        <Grid Grid.Row="1" x:Name="ContentRoot" Margin="19,9.5,19,0">
            <StackPanel>
                <Button x:Name="btnFacebookLogIn"
                Margin="50,10,50,10" 
                HorizontalAlignment="Stretch"
                Click="btnFabookLogin_Click">
                    <Grid>
                        <Grid.ColumnDefinitions>
                            <ColumnDefinition Width="1*"/>
                            <ColumnDefinition Width="2*"/>
                        </Grid.ColumnDefinitions>

                        <Image Source="ms-appx:///Assets/Images/Facebook.png"
                        Stretch="Uniform"
                        Margin="10"
                        HorizontalAlignment="Stretch"
                        VerticalAlignment="Stretch"/>
                        <TextBlock Margin="10" Grid.Column="1" 
                    VerticalAlignment="Center"
                    Text="Facebook Login"/>
                    </Grid>
                </Button>
                <TextBox x:Name="txtFbToken" 
                    Margin="50,0,50,0" 
                    PlaceholderText="facebook token" 
                    IsReadOnly="True" 
                    Height="340" 
                    TextWrapping="Wrap"/>
            </StackPanel>
        </Grid>
    </Grid>
</Page>

BasicPageFB.xaml.cs

//Code to add into BasicPageFB.xaml.cs
//this file must be previously generated by Visual Studio 2013 as new BasicPage

FacebookManager facebookManager = new FacebookManager();
private void btnFabookLogin_Click(object sender, RoutedEventArgs e)
{
    facebookManager.LoginAndContinue();
}

public void ContinueWithWebAuthenticationBroker(Windows.ApplicationModel.Activation.WebAuthenticationBrokerContinuationEventArgs args)
{
    txtFbToken.Text = facebookManager.ContinueAuthentication(args);
}

ContinuationManager.cs

using WABAndContinueDemo.Misc;
using Windows.ApplicationModel.Activation;
using Windows.UI.Xaml;
using Windows.UI.Xaml.Controls;

namespace WABAndContinueDemo.Manager
{
    class ContinuationManager
    {
        public void ContinueWith(IActivatedEventArgs args)
        {
            var rootFrame = Window.Current.Content as Frame;
            if (rootFrame == null)
                return;

            switch (args.Kind)
            {
                case ActivationKind.PickFileContinuation:
                    break;
                case ActivationKind.PickFolderContinuation:
                    break;
                case ActivationKind.PickSaveFileContinuation:
                    break;
                case ActivationKind.WebAuthenticationBrokerContinuation:
                    var continuator = rootFrame.Content as IWebAuthenticationBrokerContinuable;
                    if (continuator != null)
                        continuator.ContinueWithWebAuthenticationBroker((WebAuthenticationBrokerContinuationEventArgs)args);
                    break;
                default:
                    break;
            }
        }
    }
}

FacebookManager.cs

using System;
using System.Diagnostics;
using System.Text.RegularExpressions;
using Windows.ApplicationModel.Activation;
using Windows.Foundation.Collections;
using Windows.Security.Authentication.Web;

namespace WABAndContinueDemo.Manager
{
    class FacebookManager
    {
        readonly string _facebookUrl = "https://www.facebook.com/dialog/oauth?client_id={app-id}&redirect_uri={redirect-uri}&scope=publish_actions&display=popup&response_type=token";
        Uri _facebookUri, _callbackUri;
        const string APP_FACEBOOK_ID = "YOUR FACEBOOK ID";

        public FacebookManager()
        {
            _callbackUri = WebAuthenticationBroker.GetCurrentApplicationCallbackUri();
            Debug.WriteLine(_callbackUri);
            _facebookUrl = _facebookUrl.Replace("{app-id}", APP_FACEBOOK_ID).Replace("{redirect-uri}", _callbackUri.AbsoluteUri);
            _facebookUri = new Uri(_facebookUrl);
        }

        public void LoginAndContinue()
        {
            var continuationData = new ValueSet();
            continuationData.Add("login-type", "facebook");

            WebAuthenticationBroker.AuthenticateAndContinue(_facebookUri,
                _callbackUri, continuationData,
                WebAuthenticationOptions.None);
        }

        public string ContinueAuthentication(WebAuthenticationBrokerContinuationEventArgs args)
        {
            if (args.WebAuthenticationResult.ResponseStatus == WebAuthenticationStatus.Success)
            {
                var match = Regex.Match(args.WebAuthenticationResult.ResponseData, "access_token=(?<our_token>.+?)&+");
                var token = match.Groups["our_token"];

                return token.Value;
            }

            return string.Empty;
        }

    }
}

IWebAuthenticationBrokerContinuable.cs

using Windows.ApplicationModel.Activation;

namespace WABAndContinueDemo.Misc
{
    interface IWebAuthenticationBrokerContinuable
    {
        void ContinueWithWebAuthenticationBroker(WebAuthenticationBrokerContinuationEventArgs args);
    }
}