При создании анимации вы хотите создать обратный вызов события Completed.
...
System.Windows.Media.Animation.Storyboard storyBoard = (System.Windows.Media.Animation.Storyboard)FindResource("storyboardName");
storyBoard.Completed += new EventHandler(storyBoard_Completed);
BeginStoryboard(storyBoard);
...
void storyBoard_Completed(object sender, EventArgs e)
{
System.Windows.Media.Animation.Storyboard storyBoard = (System.Windows.Media.Animation.Storyboard)FindResource("nextAnim");
BeginStoryboard(storyBoard);
}