Hi folks!
With the 3.10.0 release of KendoReact we added in the new Drawer component which I believe covers the needs described in this thread. Please give it a try and let us know if this was indeed what you were looking for!
I'm going to go ahead and leave this item as "approved" for now, but will mark this as complete down the line if I don't hear any news around the Drawer not fulfilling the requirements of a responsive menu with a hamburger icon.
Regards,
Carl
Progress Telerik