dQ/dt = kA(T1-T2)/L applies to energy transfer (Heating) by conduction
through slabs of material of area A and thickness L. This relation is valid for
the steady state situation, T1, T2 and dQ/dt constant.
There are several possible sources of confusion in the mind of the author
of the answer key, eg confusing GOOD insulator (low k, high temperature
gradient) with GOOD conductivity (high k, low gradient), or identifying
the "slope" as dQ/dt rather than (T1-T2)/L.
Note that the temperature gradient is proportional to 1/k.