Best connection you get trough Jakarta or Singapore and from there to Balikpapan.
There is also a new early morning flight operated by Batik air directly to Berau from Jakarta
From Balikpapan take a flight to Berau with Garuda Indonesia, Transnusa, Sriwijaya Air or Wings Air. During the flight you enjoy the wonderful rain forest of Kalimantan from the bird's perspective.
After one hour flight you will land somewhere in the middle of the jungle in Berau.