Amla was 65 not out, having become just the fourth South African after Jacques Kallis, Graeme Smith and AB de Villiers to score 8,000 Test runs, and free-scoring left-hander de Kock, promoted to number four, 68 not out.
Their partnership was so far worth 113.
South Africa's sound position was a vindication of returning captain Faf du Plessis's bold call to bat first after winning the toss, with the Proteas 1-0 down in the four-match series after a 211-run defeat inside four days at Lord's last week.
Trent Bridge has a reputation for aiding swing bowling and Du Plessis, who did not play at Lord's following the birth of his first child, admitted it had been a "tricky decision" to bat under cloudy skies.
South Africa did lose an early wicket, however, when Dean Elgar, their stand-in captain at Lord's, pushed out on six to James Anderson and was well caught by a diving Liam Dawson at backward point to leave the Proteas 18 for one.
Amla, meanwhile pulled fast bowler Mark Wood for a four that saw him to 8,000 Test runs.
Kuhn was still on his interval score when he played on to Stuart Broad, striking on his Nottinghamshire home ground, to end a two-hour innings.
- Classy Amla -
Amla, who made the South African record Test score of 311 not out against England at The Oval five years ago, was, however, in fine touch.
He forced Anderson off the back foot square on the offside for four and cover-drove Broad for another boundary.
But Amla, out for meagre scores of 29 and 11 at Lord's, completed a 93-ball fifty in style on Friday when he drove left-arm spinner Dawson for a straight six.
Left-hander de Kock was also severe on Dawson, late- cutting and driving the Hampshire bowler for two well-struck fours.
Amla though did have a reprieve on 56 when former England captain Alastair Cook could not hold a very low chance at first slip from an edge off Ben Stokes.
De Kock justified his promotion with a brisk 59-ball fifty including five fours.
Fast bowler Duanne Olivier, playing in his second Test, started instead of Kagiso Rabada, serving a one-match suspension as a result of swearing at Stokes at Lord's.
England were unchanged from the XI that marked Joe Root's first match as captain with a thumping win in which the new skipper scored 190.
All South Africa's batsmen wore black armbands in memory of the late mother of Proteas coach Russell Domingo after she died recently following injuries sustained in a car crash.
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