I changed Lennard-Jones potential in example/KAPPA/in.heatflux to Mie
potential using following lines:

pair_style mie/cut ${rc}

pair_coeff 1 1 1.0 1.0 12.0 6.0

For 12/6 exponents, the formula of Mie potential is the same as
Lennard-Jones potential. But the result are totally different,

the average conductivity result with Mie potential is 3.38457528, while
Lennard-Jones potential is 4.4599338. I ran again, the

difference stayed the same.

Can anyone tell me the reason? Is it OK?

a quote from the README file:

"""
These scripts are provided for illustration purposes. No guarantee is
made that the systems are fully equilibrated or that the runs are long
enough to generate good statistics and highly accurate results.
"""

so try rerunning the lj/cut variant with several different random
number seeds for the velocity command or with a different number of
processors.
in both cases, you will get diverging trajectories (same as with
switching lj/cut and mie/cut) and thus will have resulting different
numerical results and thus highlighting the statistical variance and
thus the error bar of these numbers.

on my machine i get:
with 1 processor: 4.1226665610359596315
with 2 processors: 4.7968259591278146203
with 4 processors: 3.5682391304468636939

after changing the random number seed, i get:

with 4 processors: 3.16548078117364

so, statistically speaking, the result is approximately 4.0 with a
variance of about 0.5.