The flyout doesn't change its theme from light to dark. I don't know why. See my Example Code below. You can change the theme here and then the flyout remains in light theme.
MainPage.xaml
<Page>
<Page.BottomAppBar>
<CommandBar>
<AppBarButton Icon="Emoji">
<AppBarButton.Flyout>
<Flyout/>
</AppBarButton.Flyout>
</AppBarButton>
<AppBarToggleButton Checked="Checked" Unchecked="Unchecked">
<AppBarToggleButton.Icon>
<FontIcon Glyph="" />
</AppBarToggleButton.Icon>
</AppBarToggleButton>
</CommandBar>
</Page.BottomAppBar>
</Page>
MainPage.cs
public sealed partial class MainPage : Page
{
private void Checked(object sender, RoutedEventArgs e)
{
this.RequestedTheme = ElementTheme.Dark;
}
private void Unchecked(object sender, RoutedEventArgs e)
{
this.RequestedTheme = ElementTheme.Light;
}
}