If I want to change the units of my diffusion coefficient from $\dfrac {m^2}{\text {day}}$ to $\dfrac {km^2}{\text {day}}$, is correct to do:
$$2964660 \frac{m^2}{\text{day}} = 2964660 \frac{(0.001 km)(0.001 km) }{\text{day}} = 2.964660 \frac{km^2}{\text{day}}$$
Yes. One km$^2$ is a square with side 1 km length, so it contains 1000 rows of 1000 ( that is 1 million) squares of 1 m length.