The gateway to Tanjung Puting National Park is Pangkalan Bun. The most common way to get to Pangkalan Bun is by flying to the airport in Pangkalan Bun (Iskandar Airport). Currently, there are direct connections from Jakarta, Semarang, Surabaya in Java, and from Ketapang and Palangkaraya in Kalimantan.
A popular destination near Pangkalan Bun is Banjarmasin. There are no direct flights currently, and the most common way to get from Banjarmasin to Pangkalan Bun is by flying via Semarang. The more adventurous option is to first take the bus to Palangkaraya (±5 hours) and then continue by air.
You could use SkyScanner to search and book both the international flights to Indonesia as well as the domestic flights to Pangkalan Bun.