The left-hander made 208 off 251 balls, including 26 fours, and shared a stand of 171 with skipper Alex Wakely (73).
Kent fought back well after the home side reached 347-4, taking the last six wickets for 37 runs to trail by 154.
But their second innings began disastrously as Rory Kleinveldt claimed 4-8 and they were 15-4 at stumps.
Daniel Bell-Drummond edged the South African's first delivery to the wicketkeeper, before Sean Dickson and Joe Denly went to successive deliveries in his second over.
And play ended three balls early after James Tredwell, one of two nightwatchmen at the crease for Kent, was caught behind.
Should they lose the match, leaders Essex would only need six points from next week's game against Glamorgan to secure the sole promotion place from Division Two.
However, the day was dominated by Duckett, who boosted his chances of an England call-up this winter with a superb innings lasting just 15 minutes short of six hours.
Essex's Nick Browne is the only other batsman to have made two double hundreds this summer - both of them against Derbyshire.
Ben Duckett made his second double century of the season as Northants continued to have the upper hand against Kent on day two at Beckenham.