The Australian 15th seed received a warning from umpire Jake Garner at the start of the third set after complaining about a decision and he completely lost his head before reaching the third round with a 6-7(3-7), 6-1, 2-6, 6-4, 6-4 victory.
Asked afterwards whether his antics were distracting for other players, Kyrgios lost his cool.
"What did I say to the umpire today?" he said.
When reminded by another reporter that he told American Garner he had done a "horrible job", Kyrgios said: "Is that bad language? Have you never said a swear word before? Have you never said a swear word in your life?
"Can you answer my question?"
At which point the reporter told Kyrgios that it was his job to answer questions.
"No, it's not. He actually asked me the question. It's his question, mate. It's his question," he said.
"What did I say to the umpire today? So how is that going to affect another player by saying 'horrendous job'?
"I think you can figure that out, champ."
Kyrgios courted controversy at Wimbledon last year when he was accused of "tanking" during a match against Richard Gasquet, and also received a suspended ban from the ATP after an incident during a match with Stan Wawrinka in Montreal.
He was fined $3,380 for unsportsmanlike conduct in his opening match at Wimbledon against Radek Stepanek after raising the ire of the umpire.
At one point during his match against wildcard Brown, who is one of his friends on the Tour, a member of the public told Kyrgios to stop "behaving like a baby".
But Brown leapt to the Australian's defence.
"I'm pretty sure everyone that knows Nick, knows Nick is a great tennis player," he said.
"If certain things happen and there are a few bad calls, I mean, all of us have gotten upset on the court already for bad calls, especially in certain moments.
"I'm almost close to 10 years older. I was definitely not any better or worse at 21.
"The guy is [ranked] 18 in the world. The guy is 21. Let the guy play tennis.
"I'm pretty sure in a few years, he will also have that sorted and going to be even better."
Meanwhile, Australian qualifier Matt Barton was eliminated Wimbledon following a second-round loss to American 18th seed John Isner.
Barton, who briefly retired two years ago with a troublesome knee injury, pushed Isner to three tie-breaks in their second-round clash but was unable to get the best of the American, who sent down 43 aces to win 7-6 (10-8), 7-6 (7-3), 7-6 (10-8) in two hours and 17 minutes.