You can add that behavior to your Dock by adding the following code to your instance:
To help illustrate this, I've written a sample application that demonstrates the behavior.
Open the app and run it, you'll see two instances of Dock on MainPage.xaml. The one the left uses the built-in ClickFlyoutBehavior. The dock on the right will show you how to add animation to the flyout via the AnimatedClickFlyout behavior class.
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