Sarah Wilson was one shot from becoming the first female to make the Queensland Open cut, while David Bransdon will lead by one entering the third round at Pelican Waters.
Wilson, 19, was the second female to qualify in the tournament's 95-year history earlier in the week and paired rounds of 74 and 72 to finish two-over on her home course and just one shot behind the cut line.
Bransdon bettered the existing course record by two shots on Thursday in carding a nine-under 63.
He came back to earth with a trio of bogeys on Friday but still managed a three-under 69, a birdie on the 18th to finish one clear of Kennedy (65, 68).
Jake Higginbottom equalled Kennedy's opening-round 63, mixing eight birdies and an eagle with one bogey to shoot to eight-under after a one-over start on Thursday.
Amateur pair Josh Armstrong (65, 69) and Jack Thompson (65, 70) are 10 and nine-under respectively while defending champion Jordan Zunic missed the cut at three-over.