Healy, a former AFL player, blasted the footwork of Kokkinakis, saying it was awful compared to that of Roger Federer. Healy also said it's better to ignore Kyrgios until he "wakes up to himself" and questioned why the Canberra product doesn't have a "chip return".
Healy also believes the 23-year-old needs a coach, but Kyrgios fired back in a series of tweets.
"You blokes all have zero idea," Kyrgios wrote. "It's comical people like yourself have an opinion of us. You blokes are anything but athletes, so how about you concentrate on your owns***. Zero credibility."
Rasheed was part of the discussion and after Kyrgios hit out at Healy, he also mentioned the Aussie coach.
His second tweet was followed by laughing face emojis.
Rasheed was not critical of Australia's players and instead spoke largely about the technical and mental aspects of being a professional tennis player.
Tomic attacked Davis Cup captain Lleyton Hewitt this week but Kyrgios refused to weigh in on the feud at a post-match press conference following his loss to Milos Raonic. However, he took to Instagram on Wednesday night to slap Hewitt during Aussie Alex de Minaur's match against Swiss star Henri Laaksonen.
Tomic blasted Hewitt for not supporting Kyrgios or Kokkinakis and Kyrgios' Instagram post sided with that argument.
"Who's (sic) match is he watching. Demon, no one else," Kyrgios wrote as Hewitt watched the teenager's clash from the stands while providing special comments for Channel 9.
Hewitt was sitting courtside during Kyrgios's first round loss to Raonic on Tuesday night — but it does not appear to have satisfied the 23-year-old star.
On Tuesday Kyrgios said there is "not really" a rift between himself and Hewitt. However, his support for Hewitt appeared begrudging at best.
When asked if he supports Hewitt, Kyrgios only said with a casual shrug of his shoulders: "Sure."
It came after Tomic sensationally declared both Kokkinakis and Kyrgios recently told him that they do not want to play Davis Cup while Hewitt remains captain.
Kyrgios has since said he will make himself available for next month's tie.
However, he also said he is not "upset" that Tomic dropped his name as one player who does not support Hewitt's captaincy.