Dickson carried his bat for 207 not out, as Shiv Thakor's maiden five-wicket haul saw Kent all out for 412.
Derbyshire's Billy Godleman retired hurt without facing a ball after he was hit by a throw, before Chesney Hughes was bowled by James Tredwell for one.
Matt Coles then dismissed Tom Taylor and Hamish Rutherford for ducks.
Dickson resumed batting without Joe Denly, who retired overnight after the birth of his child, but remained unfazed throughout the day as he reached his century off 243 balls.
The 24-year-old accelerated after going past three figures and made his second 100 runs off only 107 balls.
Despite a first-innings deficit of 80, Coles trapped Taylor in front and had Rutherford caught behind to gives the visitors hope of claiming an unlikely victory on day four.
Kent batsman Sean Dickson told BBC Radio Kent:
"I've scored a first class hundred before, but scoring a Championship hundred was wonderful.
"I came up with a game plan that anything straight I would look to defend and hit it back straight, then anything slightly wider to attack.
"Luckily I had Colesy and Mitch Claydon with me there at the end and it was a lovely experience to put up 200.
"The boys are very positive - we mentioned Leicestershire getting bowled out for 40 by Worcestershire in the changing room - so, anything can happen."
Sean Dickson scored a career-best double century for Kent before Derbyshire slipped to 9-3 at the close on day three, leading by 89 runs.