I can’t comment on your units or the physicality of defining a local heat flux in this manner.
But you can do this to check your implementation:
a) run it with a single chunk and compare the result to what compute heat/flux gives
b) dump the atom variable Jz to a dump file every N steps
do the averaging yourself (post-processing) to see if it gives you meaningful results,
and to verify it gives answers consistent with the fix ave/chunk output
Steve