If you have a HUSZBZ-1 or Telegenisis Ember based controller (perhaps others) you can upgrade it using a different tool. See HUSBZB-1 (Combo Zigbee and ZWave stick) Should I bother flashing its firmware to latest?.
I just upgraded my HUSZBZ-1 and it worked great. Took all of ten minutes with another 20 minutes spent submitting a PR to add instructions to the binding README.
But back to the main topic at hand, unless it is otherwise noted in the Zigbee binding’s readme, flashing or even upgrading the coordinator is not required to work with the binding. But if upgrades are available and supported it is highly encouraged.