How do I access a control inside a XAML DataTemplate?

The problem you are experiencing is that the DataTemplate is repeating and the content is being generated by the FlipView. The Name is not exposed because it would conflict with the previous sibling that was generated (or the next one that will be).

So, to get a named element in the DataTemplate you have to first get the generated item, and then search inside that generated item for the element you want. Remember, the Logical Tree in XAML is how you access things by name. Generated items are not in the Logical Tree. Instead, they are in the Visual Tree (all controls are in the Visual Tree). That means it is in the Visual Tree you must search for the control you want to reference. The VisualTreeHelper lets you do this.

Now, how to do it?

I wrote an article on this because it is such a recurring question: http://blog.jerrynixon.com/2012/09/how-to-access-named-control-inside-xaml.html but the meat of the solution is a recursive method that looks something like this:

public void TestFirstName()
{
    foreach (var item in MyFlipView.Items)
    {
        var _Container = MyFlipView.ItemContainerGenerator
            .ContainerFromItem(item);
        var _Children = AllChildren(_Container);

        var _FirstName = _Children
            // only interested in TextBoxes
            .OfType<TextBox>()
            // only interested in FirstName
            .First(x => x.Name.Equals("FirstName"));

        // test & set color
        _FirstName.Background = 
            (string.IsNullOrWhiteSpace(_FirstName.Text))
            ? new SolidColorBrush(Colors.Red)
            : new SolidColorBrush(Colors.White);
    }
}

public List<Control> AllChildren(DependencyObject parent)
{
    var _List = new List<Control>();
    for (int i = 0; i < VisualTreeHelper.GetChildrenCount(parent); i++)
    {
        var _Child = VisualTreeHelper.GetChild(parent, i);
        if (_Child is Control)
            _List.Add(_Child as Control);
        _List.AddRange(AllChildren(_Child));
    }
    return _List;
}

The key issue here is that a method like this gets all the children, and then in the resulting list of child controls you can search for the specific control you want. Make sense?

And now to answer your question!

Because you specifically want the currently selected item, you can simply update the code like this:

if (MyFlipView.SelectedItem == null)
    return;
var _Container = MyFlipView.ItemContainerGenerator
    .ContainerFromItem(MyFlipView.SelectedItem);
// then the same as above...