In the Jabba's Realm story mission Trophy Hunting, Kallenn's mission rules state that he performs an additional action each activation and can perform multiple attacks each activation. I read this to mean that he could attack three times on his activation if he doesn't do anything else. Is this how you all read it?

Yup. Not that he's the best attacker; you're probably better off running away (12 spaces!!), as that makes it very difficult for the heroes to chase you down and kill you on that big map.

When I played he even flirted with danger by running up and ordering the rancor, and then running away

Yes, Kallenn can spend all three actions for attacking. Like @Stompburger says though, depending on the location and speed of the heroes and their activation order, and the location of the other big bad, he may be better off Attacking once and Moving twice.