The primary problem is that you set your UserControl’s DataContext to itself in its constructor:
DataContext = this;
You should not do that, because it breaks any DataContext based Bindings, i.e. to a view model instance that is provided by property value inheritance of the DataContext property
Instead you would change the binding in the UserControl’s XAML like this:
<TextBox Text="{Binding SelectedFile,
RelativeSource={RelativeSource AncestorType=UserControl}}" />
Now, when you use your UserControl and write a binding like
<userControls:FileBrowserControl SelectedFile="{Binding SelectedFile}" />
the SelectedFile property gets bound to a SelectedFile property in your view model, which should be in the DataContext inherited from a parent control.