Federer, who had a first round bye as the tournament's top seed, took just 55 minutes to see off Kamke, playing in the main draw of an ATP tournament for the first time since April.
The Swiss maestro had been suffering from the flu earlier in the week but showed no signs of illness in a commanding performance at the Pat Rafter Arena.
He asked organizers to put his first match back a day, and said he only started to feel better on Wednesday morning.
The defending champion smashed 18 winners past Kamke, who struggled from the outset against the world number three and only had one break point on Federer's serve throughout the match.
Federer will next meet Bulgaria's Grigor Dimitrov in the quarterfinals, a rematch from last year's semifinal, which Federer won comfortably.
"I played great against him last year here," Federer said.
"Tomorrow is going to be tougher," he said.
Federer acknowledged the last few days had been rocky.
"I don't quite know what to expect quite yet," the Basel native said.
"Today was thankfully short, but it also doesn't give me as much information as where my game is at," he said.
"In practice it's been great — I have been hitting the ball well. I am where I want to be," Federer said.
"Tomorrow we'll see," he said.
"He's (Dimitrov) had a tough grind today, but he's extremely match-tough."
Dimitrov earlier survived a three-set epic against Serbia's Viktor Troicki 5-7, 7-6 (8/6), 6-2.
"I think I was definitely struggling a little bit at the beginning of the match," he said.
"But it was good — it was a good match for me," Dimitrov said.
"And I'm happy that after two hours, 45 minutes my body felt really well," he said.
"I took the heat pretty good."
Fourth seeded Canadian Milos Raonic was pushed all the way by Croatian qualifier Ivan Dodig before eventually winning 6-7 (2/7), 6-1, 6-4 in almost two and a half hours.
Raonic, who reached a career ranking of four last May, dropped back to 14 after injury problems later in the year saw him withdraw from the French Open then miss the last three weeks of the season.
He said he was finally playing injury free for the first time in nine months.
"I'm further along than where I was (last year)," he said.
"I think I just sort of need matches like today to sort of reset myself."
Raonic next takes on Lucas Pouille after the Frenchman ousted sixth seeded Belgian David Goffin 7-6 (7/5), 4-6, 6-3.