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

Here is Why You Need An Adapter

The outlet and plug type used in Swaziland is M and in Brunei is G. This is how they look like.

Brunei

In Brunei, outlets of type G are in use.

Type G

Swaziland

In Swaziland, outlets of type M are in use.

Type M