Kent 164 (Leaning 34, Cox 34, Allison 4-40) and 137 for 8 (Cook 6-33) trail Essex 573 (Khushi 164, Critchley 90, Cook 78, Westley 54, Allison 53) by 272 runs
Kent’s top scorer, Jordan Cox, was not out on 53 at stumps, partnered by Matt Milnes unbeaten on 12, but Kent’s only realistic hope of avoiding defeat is if the weather intervenes on day four.
Earlier Ben Allison took 4 for 40 as Kent were dismissed for 164 in their first innings, 409 behind the 573 Essex made after they were put in on day one.
Kent were 74 for 4 when play began after a 10-minute rain delay and after some early resistance they rapidly faded.
Jack Leaning batted for 41 minutes with Cox, before Cook had him caught by a tumbling Feroze Khushi at square leg, and from then on no partnership lasted for more than five overs.
Sam Billings batted despite a groin injury, with Ben Compton acting as his runner, but he was visibly struggling and lasted just nine balls before he nicked Allison to Rossington.
Allison then removed Grant Stewart, who edged the seventh ball he faced behind for two and Harry Podmore, who made 13 before he became Rossington’s fifth victim of the innings.
Allison then clipped the top of Cox’s off stump, bowling him for 34, before the rain returned, with Kent 145 for 9, ushering in an early lunch.
When play resumed Matt Quinn tried to hit Shane Snater out of the ground and was bowled for 7, leaving Essex with a mammoth first-innings lead.
To the surprise of precisely no one in the Spitfire Ground they enforced the follow on, claiming an early victim when Ollie Robinson edged Cook behind for 15, before a second rain delay wiped out 19 overs.
Kent’s best hope of salvaging a draw lay in batting out the day and hoping a grim weather forecast for day four would prove accurate, but when play resumed Cook hadn’t even completed his over before he’d removed Daniel Bell-Drummond for a second-ball duck, again caught behind.
In Cook’s next over he took wickets with successive deliveries, first getting Ben Compton caught at second slip by Matt Critchley for 7, then getting Leaning caught for a golden duck by the same fielder.
Cook claimed his fifth wicket of the innings when Joe Denly tried to pull him and instead got a top edge that floated to Nick Browne at third slip. Stewart tried to drive Cook and was caught by Browne at mid off for six.
Harry Podmore lingered for 46 balls for 10 before he was bowled by Jamie Porter and Essex looked like wrapping up the win inside three days when Billings chipped the same bowler to Tom Westley, for his first ever pair, but Cox pulled Snater for four to pass 50 shortly before the scheduled close and although the extra half hour was taken, the players went off for bad light at 6.59 pm.