I could not find a way to bind my commands to the hamburger menu yet. Additional details could also be found at https://stackoverflow.com/questions/46333978/mvvm-command-binding-to-uwp-toolkit-hmaburger-menu
I believe @bartlannoeye's answer is correct. Closing the issue.
I know you closed this topic. But I still think would it be better if you can just add direct support to have
<controls:HamburgerMenu x:Name="hamburgerMenuControl"
Grid.Row="0"
Grid.Column="0"
PaneBackground="Black"
Foreground="White"
DisplayMode="CompactOverlay"
ItemsSource="{Binding Path=MainMenuItems}"
ItemTemplate="{StaticResource DefaultTemplate}"
ItemClickedCommand="{Binding Path=ItemCommand}"
OptionsItemsSource="{Binding Path=OptionMenuItems}"
OptionsItemTemplate="{StaticResource DefaultTemplate}"
OptionsItemClickedCommand="{Binding Path=ItemCommand}">
<Frame x:Name="contentFrame" />
</controls:HamburgerMenu>
@HardySoftware as this control will be deprecated (because of the NavigationView control in Fall Creators Update, there won't be any additions, see https://github.com/Microsoft/UWPCommunityToolkit/issues/653.
But since this is all open source, you could for the code add them yourself (and use your own forked control).