Should a stove flue be grounded for lightning protection?
A lightning protection system is a building wide system.

You don't just protect things individually.

The ridgeline of your house would get air terminals and then if the antenna and chimney are within the "zone of influence" (lightning protection term) they would be bonded to the system.

If your house is less than 50' tall and you are not in an extremely high strike area (central Florida), I wouldn't bother. Usually very tall barns are the only residential buildings that get lightning protection. 

Good luck!