You Do Need power plug adapter while traveling from Burundi to South Sudan.

Here is Why You Need An Adapter

The outlet and plug type used in South Sudan are C and D and in Burundi are C and E. This is how they look like.

Burundi

In Burundi, outlets of type C and E are in use.

Type C

Type E

South Sudan

In South Sudan, outlets of type C and D are in use.

Type C

Type D