The 39-year-olds blitzed an opening stand of 160 to propel the Thunder to 208-1, the sixth highest score in Big Bash history and the best in their team???s history.
When Hussey (96 off 60) and Kallis (97no off 55) were finally separated having taken 25 runs off Flintoff???s two overs, England???s new one-day captain Eoin Morgan hit 12no off five balls.
Lancastrian Flintoff, batting at seven, then fell for a third-ball duck as the Heat folded to 152 all out off 17.5 overs after losing six wickets of 19 runs.
The Thunder went into the contest having won just one game in the previous two years but dominated from the off as Kallis and Hussey cut loose.
Flintoff entered the attack in the sixth over and was pulled into the stands for six by Hussey as the 50-stand came up inside the Powerplay.
Hussey posted his fifty off 35 balls, Kallis reaching his own half-century off 37 balls after picking up six more over square leg when Flintoff returned for his second over in the 14th.
Neither veteran could go on and post a hundred, however, Hussey???s innings coming to an end when he skied Cameron Gannon and wicketkeeper Jimmy Peirson clinging onto the chance.
His downfall brought Morgan to the crease with three overs to go and the left-hander struck his first boundary in unorthodox fashion, stepping deep in his crease to steer the ball between himself and leg stump and away past Peirson to the rope.
Kallis had a chance to post his first T20 century but finished unbeaten on 97 after failing to strike the boundary he needed to reach three figures off the final ball of the innings.
The South African all-rounder quickly proved his credentials with the ball, removing Daniel Christian with his second ball to reduce the Heat to 14.2 off 2.2 overs following the first over dismissal of Simon Milenko, who was out for a duck on his debut.
Joe Burns, called into Australia???s squad for the Boxing Day Test against India, was struck early on in his innings in the midriff by Dirk Nannes.
The 25-year-old showed no ill-effects, though, as he struck six fours while adding 59 for the third wicket with Chris Lynn before picking out Kallis at deep midwicket to go for 28 off 23 balls.
Lynn (40 off 26) and Nathan Reardon (49 off 25) battled to get the Heat back on terms but had little support.
Flintoff walked to the wicket with his side 133-5 needing 76 runs off 33 balls but couldn???t turn the tide as he picked out Gurinder Sandhu (3-19) attempting to drive Andrew McDonald (3-20) over long-off.