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.
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.
At lunch, South Africa were 56 for one with opener Heino Kuhn 34 not out, after being twice dismissed for single figures on debut at Lord's, and Amla unbeaten on 16.
- 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.
Prior to this series, South Africa batting great Barry Richards suggested that, at the age of 34, Amla's best days might be behind him.
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.
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.
South Africa made three changes to their side, with Du Plessis returning in place of out-of-form batsman JP Duminy.
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.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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