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

Here is Why You Need An Adapter

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

Brunei

In Brunei, outlets of type G are in use.

Type G

Kiribati

In Kiribati, outlets of type I are in use.

Type I