How do I access a page frame to navigate a page through a UserControl object in a UWP?

We can let the page to navigate itself. Just define an event in your custom usercontrol and listen to the event in its parent(the page).

Take the following as an example:

1. Create a custom user control and put a button on it for test purpose.
2. In test button's click event, raise the event to navigate parent page.
3. In Parent page, listen to the UserControl's event and call Frame.Navigate.

MyControl's Xaml:

<UserControl
x:Class="App6.MyControl"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:local="using:App6"
xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
mc:Ignorable="d"
d:DesignHeight="300"
d:DesignWidth="400">

<Grid>
    <Button x:Name="testbtn" Margin="168,134,0,134" Click="testbtn_Click">test</Button>
</Grid>
</UserControl>

MyControl's CodeBehind:

public sealed partial class MyControl : UserControl
{

    public delegate void MyEventHandler(object source, EventArgs e);

    public event MyEventHandler OnNavigateParentReady;

    public MyControl()
    {
        this.InitializeComponent();
    }

    private void testbtn_Click(object sender, RoutedEventArgs e)
    {
        OnNavigateParentReady(this, null);
    }


}

Navigate MainPage to SecondPage:

    public MainPage()
    {
        this.InitializeComponent();

        myControl.OnNavigateParentReady += myControl_OnNavigateParentReady;
    }

    private void MyControl_OnNavigateParentReady(object source, EventArgs e)
    {
        Frame.Navigate(typeof(SecondPage));
    }

You could get a reference to the Frame from the Current Window's Content. In your user control's code behind try:

Frame navigationFrame = Window.Current.Content as Frame;
navigationFrame.Navigate(typeof([page]));