OneWayToSource binding from readonly property in XAML

Some research results for OneWayToSource...

Option # 1.

// Control definition
public partial class FlagThingy : UserControl
{
    public static readonly DependencyProperty IsModifiedProperty = 
            DependencyProperty.Register("IsModified", typeof(bool), typeof(FlagThingy), new PropertyMetadata());
}

<controls:FlagThingy x:Name="_flagThingy" />

// Binding Code
Binding binding = new Binding();
binding.Path = new PropertyPath("FlagIsModified");
binding.ElementName = "container";
binding.Mode = BindingMode.OneWayToSource;
_flagThingy.SetBinding(FlagThingy.IsModifiedProperty, binding);

Option # 2

// Control definition
public partial class FlagThingy : UserControl
{
    public static readonly DependencyProperty IsModifiedProperty = 
            DependencyProperty.Register("IsModified", typeof(bool), typeof(FlagThingy), new PropertyMetadata());

    public bool IsModified
    {
        get { return (bool)GetValue(IsModifiedProperty); }
        set { throw new Exception("An attempt ot modify Read-Only property"); }
    }
}

<controls:FlagThingy IsModified="{Binding Path=FlagIsModified, 
    ElementName=container, Mode=OneWayToSource}" />

Option # 3 (True read-only dependency property)

System.ArgumentException: 'IsModified' property cannot be data-bound.

// Control definition
public partial class FlagThingy : UserControl
{
    private static readonly DependencyPropertyKey IsModifiedKey =
        DependencyProperty.RegisterReadOnly("IsModified", typeof(bool), typeof(FlagThingy), new PropertyMetadata());

    public static readonly DependencyProperty IsModifiedProperty = 
        IsModifiedKey.DependencyProperty;
}

<controls:FlagThingy x:Name="_flagThingy" />

// Binding Code
Same binding code...

Reflector gives the answer:

internal static BindingExpression CreateBindingExpression(DependencyObject d, DependencyProperty dp, Binding binding, BindingExpressionBase parent)
{
    FrameworkPropertyMetadata fwMetaData = dp.GetMetadata(d.DependencyObjectType) as FrameworkPropertyMetadata;
    if (((fwMetaData != null) && !fwMetaData.IsDataBindingAllowed) || dp.ReadOnly)
    {
        throw new ArgumentException(System.Windows.SR.Get(System.Windows.SRID.PropertyNotBindable, new object[] { dp.Name }), "dp");
    }
 ....

WPF will not use the CLR property setter, but seems it does some odd validation based on it.

May be in your situation this can be ok:

    public bool IsModified
    {
        get { return (bool)GetValue(IsModifiedProperty); }
        set { throw new Exception("An attempt ot modify Read-Only property"); }
    }

The way I worked around this limitation was to expose only a Binding property in my class, keeping the DependencyProperty private altogether. I implemented a "PropertyBindingToSource" write-only property (this one not a DependencyProperty) which can be set to a binding value in the xaml. In the setter for this write-only property I call to BindingOperations.SetBinding to link the binding to the DependencyProperty.

For the OP's specific example, it would look like this:

The FlatThingy implementation:

public partial class FlatThingy : UserControl
{
    public FlatThingy()
    {
        InitializeComponent();
    }

    public Binding IsModifiedBindingToSource
    {
        set
        {
            if (value?.Mode != BindingMode.OneWayToSource)
            {
                throw new InvalidOperationException("IsModifiedBindingToSource must be set to a OneWayToSource binding");
            }

            BindingOperations.SetBinding(this, IsModifiedProperty, value);
        }
    }

    public bool IsModified
    {
        get { return (bool)GetValue(IsModifiedProperty); }
        private set { SetValue(IsModifiedProperty, value); }
    }

    private static readonly DependencyProperty IsModifiedProperty =
        DependencyProperty.Register("IsModified", typeof(bool), typeof(FlatThingy), new PropertyMetadata(false));

    private void Button_Click(object sender, RoutedEventArgs e)
    {
        IsModified = !IsModified;
    }
}

Notice that the static readonly DependencyProperty object is private. In the control I added a button whose click is handled by Button_Click. The use of the FlatThingy control in my window.xaml:

<Window x:Class="ReadOnlyBinding.MainWindow"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
    xmlns:local="clr-namespace:ReadOnlyBinding"
    mc:Ignorable="d"
    DataContext="{x:Static local:ViewModel.Instance}"
    Title="MainWindow" Height="450" Width="800">
<Grid>
    <Grid.RowDefinitions>
        <RowDefinition />
        <RowDefinition />
    </Grid.RowDefinitions>

    <TextBlock Text="{Binding FlagIsModified}" Grid.Row="0" />
    <local:FlatThingy IsModifiedBindingToSource="{Binding FlagIsModified, Mode=OneWayToSource}" Grid.Row="1" />
</Grid>

Note that I've also implemented a ViewModel for binding to that is not shown here. It exposes a DependencyProperty named "FlagIsModified" as you can glean from the source above.

It works great, allowing me to push information back into the ViewModel from the View in a loosely coupled manner, with the direction of that information flow explicitly defined.

You're doing the binding in the wrong direction right now. OneWayToSource will try and update FlagIsModified on container whenever IsModified changes on the control you are creating. You want the opposite, which is to have IsModified bind to container.FlagIsModified. For that you should use the binding mode OneWay

<controls:FlagThingy IsModified="{Binding FlagIsModified, 
                                          ElementName=container, 
                                          Mode=OneWay}" />

Full list of enumeration members: http://msdn.microsoft.com/en-us/library/system.windows.data.bindingmode.aspx