You can use an additional ScaleTransform and then animate this transform if you want a smooth flipping animation.
      <Storyboard x:Key="Storyboard_Flip">
        <DoubleAnimationUsingKeyFrames BeginTime="00:00:00"
                                       Storyboard.TargetName="front"
                                       Storyboard.TargetProperty="(UIElement.RenderTransform).(ScaleTransform.ScaleX)">
          <SplineDoubleKeyFrame KeyTime="00:00:00.2" Value="0" />
        </DoubleAnimationUsingKeyFrames>
        <DoubleAnimationUsingKeyFrames BeginTime="00:00:00.2"
                                       Storyboard.TargetName="back"
                                       Storyboard.TargetProperty="(UIElement.RenderTransform).(ScaleTransform.ScaleX)">
          <SplineDoubleKeyFrame KeyTime="00:00:00.4" Value="1" />
        </DoubleAnimationUsingKeyFrames>
      </Storyboard>
And here's the reverse flip animation.
      <Storyboard x:Key="Storyboard_Reverse">
        <DoubleAnimationUsingKeyFrames BeginTime="00:00:00"
                                       Storyboard.TargetName="back"
                                       Storyboard.TargetProperty="(UIElement.RenderTransform).(ScaleTransform.ScaleX)">
          <SplineDoubleKeyFrame KeyTime="00:00:00.2" Value="0" />
        </DoubleAnimationUsingKeyFrames>
        <DoubleAnimationUsingKeyFrames BeginTime="00:00:00.2"
                                       Storyboard.TargetName="front"
                                       Storyboard.TargetProperty="(UIElement.RenderTransform).(ScaleTransform.ScaleX)">
          <SplineDoubleKeyFrame KeyTime="00:00:00.4" Value="1" />
        </DoubleAnimationUsingKeyFrames>
      </Storyboard>