The Proteas reached 514 for two at lunch on day four of the first test at The Oval on Sunday.
Amla was 251 not out and nearing his career best score of 253 (not out) that he scored against India in Nagpur two years ago. Kallis demonstrated his usual ruthlessness by piling on the agony for England's bowlers with a merciless innings of 125 not out.
The Proteas led by 129 runs at the interval in reply to England's 385 and appeared to be in no rush to bat towards a declaration as the sun shone over London and the pitch showed little evidence of deteriorating.
The bowlers initially sought to squeeze the tourists by restricting their scoring options with a straighter line and conventional field placings. But Amla and Kallis, who have added 254 for the third wicket, kept their patience and waited for the bowlers to tire and then punished the wayward deliveries.
Amla reached his second test double hundred with a cover drive off Stuart Broad for three. He has demonstrated a near faultless technique throughout his innings and the chance he offered England captain Andrew Strauss on Friday evening at first slip has been his one error.
Kallis raised his century and the 200 partnership with a push to the third man boundary off Tim Bresnan.
Only India's Sachin Tendulkar has scored more test centuries, with 51, and Kallis celebrated by pointing to his eyes, a show of solidarity for wicketkeeper Mark Boucher who was forced to retire from international cricket after suffering a serious eye injury before the series started.
England are seeking to hold on to their position at the top of the world rankings, though South Africa can leapfrog them if they win the three-match series. — Reuters.