Tom Westley's first day as captain since replacing Ryan Ten Doeschate during the winter proved tricky, with the visitors ending on 344 for six.
Kuhn's innings of 140 not out was the bedrock of a superb total for Kent, who were indebted to Ollie Robinson's 78.
Jamie Porter and Sam Cook combined for five wickets and had reduced the away side to 23 for three in the morning session, but it was downhill from there.
Before the start of play in each of the nine fixtures, squads from all 18 counties observed a minute's silence as a mark of respect for those affected by coronavirus and decided to take a knee to promote racial equality.
Kuhn was not the only man to hit a hundred in the South Group, with Nick Gubbins unbeaten 150 guiding Middlesex to 264 for four against Surrey at the Kia Oval.
A crowd of 2,500 was expected before Prime Minister Boris Johnson called off the return of fans on a pilot basis to sporting events on Friday afternoon.
Had people been in attendance, Gubbins would have been afforded huge applause after he scored only his second first-class century in three years.
Surrey's stand-in captain Rikki Clarke was the pick of the bowlers for the hosts with two for 33.
Wickets tumbled in the other South Group fixture, where Hampshire dismissed Sussex for 176 at Hove after Mason Crane and debutant Ajeet Dale claimed three wickets apiece.
Phil Salt top scored for the home side with an 83-ball innings of 68 and they fought back late in the day to reduce the visitors to 77 for four, with Ollie Robinson the pick of the bowlers with two for 29.
England bowler Olly Stone showed his class with a four-wicket haul for Warwickshire at home to Northamptonshire in the Central Group.
A disrupted first session failed to stop Ben Coad picking up four wickets after lunch to ensure the hosts were dismissed for 103 inside 59 overs at Chester-le-Street.
Yorkshire had almost reduced the deficit by the close but the wicket of Tom Kohler-Cadmore after a run-a-ball 41 briefly halted their momentum as they finished on 84 for four.
Lancashire captain Dane Vilas fell 10 short of a century after he helped his side fight back from a poor start at their temporary base of New Road.
With Emirates Old Trafford being used by England for their Test series with Pakistan, the Red Rose are without a home, but ended an encouraging day one against Leicestershire on 265 for six after Steven Croft added 63.
Ex-Lancashire opener Haseeb Hameed struck 68 on his first appearance for new county Nottinghamshire against Derbyshire.
The Trent Bridge club started well an opening partnership of 111, but Chris Nash's departure for 59 saw them collapse to 192 for seven.
It took some lusty blows from Samit Patel in his 63 to get them over the 300-mark and up to 324 before Derbyshire ended the day on nine without loss.