A traditional Maori pukuna - toungue out and eyes wide - is twice incorporated into the routine, as well as a short war cry.
The kids join in, and Mr Flavell's wife appears from a bedroom holding a baby for a short cameo.
In a message accompanying the video, Mr Flavell challenges his Co-Leader, Marama Fox, all Maori Members of Parliament and US President Barack Obama to also complete the running man challenge.
Mr Flavell said he and his staff had been watching the progress of the craze across Facebook and decided they should give it a go.
"Dancing is in my blood," he said. "No, I'm joking. I haven't been honing my moves. It was a spontaneous thing, I was about to take my grandchild back to his father and my staff turned up and said we had to do it."
Mr Flavell said he was hopeful Barack Obama would respond.
"It's a bit of a competition. If you bust your moves you've got to hope that people think they can do better," he said. "But I haven't heard from my co-leader Marama so clearly she can't hack it."
The craze began when New Zealand police first released a video of their self-described "twinkle-toed staff" on Tuesday, and challenged police counterparts around the world to take part.
They said the video had reached an astonishing 24 million people by Friday, and had been viewed 7.9 million times.
So far emergency services from New York to London to Victoria, Australia have taken up the challenge, including fire, ambulance and police.
Mr Flavell was the first to extend the challenge to the White House.
Barack, you're up.
