Example of binding MahApps.Metro Flyout IsOpen using MVVM Light

MainViewModel

using System;
using System.Collections.ObjectModel;
using System.Threading;

using GalaSoft.MvvmLight;
using GalaSoft.MvvmLight.Command;

using TrinityToolkit;

using TrinityPlayer.Model;
using Microsoft.Practices.ServiceLocation;

namespace TrinityPlayer.ViewModel
{
    /// <summary>
    /// This class contains properties that the main View can data bind to.
    /// <para>
    /// Use the <strong>mvvminpc</strong> snippet to add bindable properties to this ViewModel.
    /// </para>
    /// <para>
    /// You can also use Blend to data bind with the tool's support.
    /// </para>
    /// <para>
    /// See http://www.galasoft.ch/mvvm
    /// </para>
    /// </summary>
    public class MainViewModel : ViewModelBase
    {
        #region Private Members

        private bool mIsSettingsOpen = false;

        #endregion

        #region Public Properties

        public AccordianViewModel Accordian
        {
            get
            {
                return ServiceLocator.Current.GetInstance<AccordianViewModel>();
            }
        }

        public DisplayGridViewModel DisplayGrid
            {
            get
                {
                return ServiceLocator.Current.GetInstance<DisplayGridViewModel>();
            }
        }

        public SettingsViewModel Settings
        {
            get
            {
                return ServiceLocator.Current.GetInstance<SettingsViewModel>();
            }
        }

        public bool IsSettingsOpen
        {
            get { return mIsSettingsOpen; }
            set
            {
                mIsSettingsOpen = value;
                RaisePropertyChanged("IsSettingsOpen");
            }
        }

        public RelayCommand OpenSettings { get; set; }

        #endregion Public Properties

        #region Constructor

        public MainViewModel()
        {
            OpenSettings = new RelayCommand(() =>
            {
                IsSettingsOpen = true;
            });
        }

        #endregion

    }
}

MainWindow (MainView)

<Controls:MetroWindow x:Class="TrinityPlayer.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:Controls="clr-namespace:MahApps.Metro.Controls;assembly=MahApps.Metro"
        xmlns:v="clr-namespace:TrinityPlayer.Views"
        Title="MainWindow" Height="500" Width="700"
        DataContext="{Binding Main, Source={StaticResource Locator}}">
    <Window.Resources>
        <ResourceDictionary>
            <ResourceDictionary.MergedDictionaries>
                <ResourceDictionary Source="pack://application:,,,/MahApps.Metro;component/Styles/Colours.xaml" />
                <ResourceDictionary Source="pack://application:,,,/MahApps.Metro;component/Styles/Fonts.xaml" />
                <ResourceDictionary Source="pack://application:,,,/MahApps.Metro;component/Styles/Controls.xaml" />
                <ResourceDictionary Source="pack://application:,,,/MahApps.Metro;component/Styles/Accents/Blue.xaml" />
                <ResourceDictionary Source="pack://application:,,,/MahApps.Metro;component/Styles/Accents/BaseLight.xaml" />
            </ResourceDictionary.MergedDictionaries>
        </ResourceDictionary>
    </Window.Resources>
    <Controls:MetroWindow.WindowCommands>
        <Controls:WindowCommands>
            <Button Content="settings" Command="{Binding OpenSettings}"/>
        </Controls:WindowCommands>
    </Controls:MetroWindow.WindowCommands>
    <Controls:MetroWindow.Flyouts>
        <Controls:Flyout Header="settings" Position="Right" IsOpen="{Binding IsSettingsOpen}">
            <Grid>
                <ContentControl Content="{Binding Settings}" />
            </Grid>
        </Controls:Flyout>
    </Controls:MetroWindow.Flyouts>
    <Grid>
        <Grid.ColumnDefinitions>
            <ColumnDefinition Width="200"/>
            <ColumnDefinition Width="500*"/>
        </Grid.ColumnDefinitions>
        <ContentControl Grid.Column="0" Content="{Binding Accordian}"/>
        <ContentControl Grid.Column="1" Content="{Binding DisplayGrid}"/>
    </Grid>
</Controls:MetroWindow>