The constant $k$ in Coulomb's law depends on

The value of  $K=\frac{1}{4\pi {\epsilon }_0}=9\times {10}^{9}N{m}^2{C}^{-2}=1dynec{m}^{2}es{u}^{-2}$

where ${\epsilon }_0$  is permittivity of free space. So the value of K will depend on nature of the medium and units used.