Italy's Australian Open champion, who backed up his debut Grand Slam title by winning the 500-series Rotterdam event, motored into the third round to remain undefeated this season.
The third-ranked 22-year-old completed his 16th consecutive match victory while improving to 4-0 over Kokkinakis.
Sinner has won his last 15 meetings with Aussie opponents, last losing to one three years ago in Toronto.
The third seed broke the match open at three-all and was never threatened in his race to victory.
"It felt a little breezy and it was tough to play in the beginning," Sinner said after his 80-minute sweep comprising 21 winners and just seven unforced errors.
"I can be very happy, he is a player who serves big," the Italian added.
"It took a few games to get the feel of the court but then it felt much better for me."
Sinner ran off a dozen points in a row to earn a lead of a set and 3-0 and continued to apply the screws to his 99th-ranked opponent.
The Italian won the final 10 games to advance and will face either Jan-Lennard Struff or Borna Coric in the next round.
Alex de Minaur, the 10th-seeded winner of the Acapulco title, regained some Aussie pride as he crushed Japan's Taro Daniel 6-1, 6-2.
De Minaur lost the February Rotterdam final to Sinner.
In the women's WTA draw, reigning Wimbledon champion Marketa Vondrousova beat American Bernarda Pera with the loss of just two games.
Vondrousova took just 64 minutes to dispatch Pera 6-0, 6-2.
