WPF

1. Create a custom control. Let's call this control "StyleChangedControl".
2. StyleChangedControl will expose a custom event, StyleChanged.
3. When a StyleChangedControl constructor is called, it will subscribe itself to the static event, StyleChangedControl.ApplicationStyleChanged. We'll call this new StyleChangedControl "NewStyleChangedControl".
4. When I change the application style, I will call StyleChangedControl.NotifyOfStyleChange() (a static method).
5. NotifyOfStyleChange() will fire the StyleChangedControl.ApplicationStyleChanged event (each NewStyleChangedControl will receive notification of that event).
6. Once NewStyleChangedControl gets notification of the ApplicationStyleChanged event, it will itself raise its own StyleChanged event.
7. In the resource dictionary that declares the style that contains the button, there will be an instance of StyleChangedControl.
8. The button will have an event trigger that is subscribed to that NewStyleChangedControl's StyleChanged event.
9. When that StyleChanged event gets fired, the event trigger will recognize it, and will then initiate an animation. This will accomplish the goal of firing an animation when the application style changes.

<ResourceDictionary xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:local="clr-namespace:WpfApplication1">
    <Style TargetType="Button">
        <Setter Property="Button.Template">
            <Setter.Value>
                <ControlTemplate>
                    <Grid>
                        <local:StyleChangedControl x:Name="MyStyleChangeCon" />
                        <Rectangle>
                            <Rectangle.Fill>
                                <SolidColorBrush x:Name="rectFill" Color="Yellow" />
                            </Rectangle.Fill>
                        </Rectangle>
                        <ContentPresenter Content="{TemplateBinding Button.Content}" />
                    </Grid>
                    <ControlTemplate.Triggers>
                        <EventTrigger SourceName="MyStyleChangeCon" RoutedEvent="local:StyleChangedControl.StyleChange">
                            <BeginStoryboard>
                                <Storyboard>
                                    <ColorAnimation
                                        Storyboard.TargetName="rectFill"
                                        Storyboard.TargetProperty="Color"
                                        To="Blue"
                                        AutoReverse="True"
                                        RepeatBehavior="Forever"
                                        Duration="0:0:1" />
                                </Storyboard>
                            </BeginStoryboard>
                        </EventTrigger>
                    </ControlTemplate.Triggers>
                </ControlTemplate>
            </Setter.Value>
        </Setter>
    </Style>
</ResourceDictionary>

<Window x:Class="WpfApplication1.Window1"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    Title="Window1" Height="300" Width="300">
    <Button Click="Button_Click">Change Style</Button>
</Window>

// Main window.
public partial class Window1 : Window
{

	// Constructor.
	public Window1() {InitializeComponent();}

	// This button event changes the style.
	private void Button_Click(object sender, RoutedEventArgs e)
	{

		// Assign the new style.
		Application.Current.Resources.MergedDictionaries.Add(
			(ResourceDictionary)Application.LoadComponent(
			new Uri(@"AnimatedStyleDictionary.xaml", UriKind.Relative)));
		
		// Queue up a thread so the above style gets a
		// chance to apply before the below code executes.
		Thread t = new Thread(new ThreadStart(delegate()
		{
			this.Dispatcher.Invoke(new ThreadStart(delegate()
			{
				// Send notification that application style changed.
				StyleChangedControl.NotifyOfApplicationStyleChange();
			}));
		}));
		t.Start();

	}

}

// The sole purpose of this control is to fire the StyleChange event.
public class StyleChangedControl : Control
{

	// The static event.
	private static event ThreadStart ApplicationStyleChange;

	// The event that is on every instance of StyleChangedControl.
	public event RoutedEventHandler StyleChange
	{
		add
		{
			AddHandler(StyleChangeEvent, value);
		}
		remove
		{
			RemoveHandler(StyleChangeEvent, value);
		}
	}
	public static RoutedEvent StyleChangeEvent =
		EventManager.RegisterRoutedEvent("StyleChange",
		RoutingStrategy.Direct, typeof(RoutedEventHandler),
		typeof(StyleChangedControl));

	// Other classes call this when they change the application style.
	public static void NotifyOfApplicationStyleChange()
	{
		if (ApplicationStyleChange != null)
		{
			// Notify instances of style change.
			ApplicationStyleChange();
		}
	}

	// Constructor.
	public StyleChangedControl()
	{

		// This control does not need to be seen.
		this.Visibility = Visibility.Collapsed;

		// Subscribe instance method to static event.
		ApplicationStyleChange += this.OnStyleChange;

	}

	// Static event calls this.
	private void OnStyleChange()
	{

		// Raise event to notify all listening EventTriggers.
		RoutedEventArgs e = new RoutedEventArgs(StyleChangeEvent);
		RaiseEvent(e);

	}

}