public MainWindow()
    {
        InitializeComponent();
        FFmpegConfig.UserInterfaceManager = new FFmpegUserInterfaceManager(this); // Вот сюда.
    }

public class FFmpegUserInterfaceManager : UserInterfaceManagerBase
{
    private Window parent;

    public FFmpegUserInterfaceManager(Window parent)
    {
        this.parent = parent;
    }

    public override IUserInterface CreateUI(string title, bool autoClose)
    {
        return Application.Current.Dispatcher.Invoke(() => FFmpegWindow.Instance(parent, title, autoClose));
    }

    public override void DisplayError(FFmpegProcess host)
    {
        Application.Current.Dispatcher.Invoke(() => FFmpegErrorWindow.Instance(parent, host));
    }
}

Application.Current.Dispatcher.Invoke(() => FFmpegErrorWindow.Instance(parent, host));