How to hide wpf datagrid columns depending on a property

A column in a datagrid is an abstract object which does not appear in the visual tree, thus you cannot use RelativeSource-binding, ElementName will not work either since it will not find a governing FrameworkContentElement so you are in kind of a bind.

One way that works is via Source and x:Reference, for that you will need to name your window and move the column to its resources to avoid a cyclical dependency error:

<Window Name="_window" ...>
    <Window.Resources>
        <DataGridTextColumn x:Key="ThatPeskyColumn"
                            Binding="{Binding Size}"
                            Visibility="{Binding DataContext.Flag, Source={x:Reference _window}, Converter={StaticResource BoolToVis}}"/>
    </Window.Resources>
    <!-- ... -->
        <DataGrid AutoGenerateColumns="False" Name="Blumen" 
                  ItemsSource="{Binding Leaves}">
            <DataGrid.Columns>
                <StaticResource ResourceKey="ThatPeskyColumn"/>
                <!-- ... -->

Great fun.