You Do Need power plug adapter while traveling from Brunei to Zambia.

Here is Why You Need An Adapter

The outlet and plug type used in Zambia are C, D and G and in Brunei is G. This is how they look like.

Brunei

In Brunei, outlets of type G are in use.

Type G

Zambia

In Zambia, outlets of type C, D and G are in use.

Type C

Type D

Type G