Caine plays the title character, Matthew, a Paris-based American who has lost the love of his life to cancer and whose son, Miles (Kirk), and daughter, Karen (Gillian Anderson), have a few bones to pick over with him.
Exacerbating the conflict is Matthew's new friendship with Parisian dance instructor Pauline, played by Clémence Poésy. The flawed father further alienates his children as he struggles to find reasons to live.
So we talk about Caine; or more precisely, Kirk's impressions of his legendary co-star and how these coalesce when a younger actor is working with one of their heroes.
"Michael Caine put out an acting book and they did a video of it as well that I remember from being young," laughs Kirk. "Luckily, I had forgotten most of the tips by the time I walked on the set."
Fortunately, Kirk doesn't get star struck, which must be a challenge given the high calibre of talent he has been fortunate enough to work with in the couple of decades he has been an actor.
"I used to get intimidated by my co-workers but now I just get excited," he admits. "It's still pretty cool and surreal. The time that was the coolest for me was watching the movie for the first time.
"That was when I was able to relax and say, 'Look at you, acting in that scene with Michael Caine. That's a little bizarre'."
Although he did a 32-episode run as Bartholomew Zane in TV show Jack & Jill in the late-1990s, Angels In America was the first time Kirk found himself working in the midst of A-listers, behind and in front of the camera.
"That was the time it was sort of overwhelming," he recalls. "And I got through that. Now it's a different deal. That thing was overloaded with great things, not the least of which was the text itself. It was the play of my generation.
"Subsequently it is made into a movie and there is Mike Nicholls directing and Meryl Streep and Al Pacino and so on acting. It's almost too much to get your head around all at once.
"It's something that you learn to process. Once you get used to doing years on end of being on a set, playing your character and saying your words, you have your own kind of world that you live in. So it's great, yeah. I love it."
He also loved spending time with Caine in the hotel bar during the Mr Morgan's shoot.
"Michael was always up for a drink or two and told some great old Hollywood stories," he chuckles.
Caine's American accent in the film takes some getting used to, though Kirk is surprised a New Zealander can discern the distracting flaws in his delivery. "His voice on its own, whatever he's doing, is so identifiable, so iconic," he says.
But who does the better American accent? Caine or Crystal, the female capuchin monkey famous for both Night at the Museum movies and The Hangover Part II and Kirk's co-star in Animal Practice?
"I'm gonna plead the Fifth, as we say in America," replies Kirk, with the kind of diplomacy befitting someone with his experience in show business.
Mr Morgan's Last Love is screening now.
