What do I have to do to be able to do the quest "BUILDING THE BASE: PRISONER OF WAR"?

I need this quest to make a Elite sunspear armor, but Dunkoro won't give it to me. What do I have to do?

You get the quest from Dunkoro in the sunspear command post. Are you talking to the npc (dunkoro) there?

There are a couple of main storyline quests that have to happen first. I think it becomes available after rescuing Koss...if not then just keep doing primary quests until it becomes available.

Have you taken the 'The Command Post' quest from Lonai in Sunspear Sanctuary? Not sure if it's strictly a requirement but you were intended to have it when doing that quest.