New Zealand collapsed to 120 all out in their second innings in the first Test in Centurion, which South Africa won by 128 runs.
"We've got to get more runs on the board, that's been something that has concerned the side for a number of Tests," Fleming told a news conference on Wednesday.
"We've been able to bowl well enough to win matches against the West Indies and to compete against other sides but we've got to consistently get more runs from the top order.
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The Newlands pitch is showing bare patches and Fleming said New Zealand could consider adding off spinner Jeetan Patel to their attack as a backup for Daniel Vettori.
"We think there are enough options with our all-rounders to accommodate a second spinner," he said.
Fleming said fast bowler Shane Bond, who will miss yet another Test through injury, was not expected to be out of action long.
"It's an inflammation injury that will settle down with a period of rest, we haven't been able to get him enough rest," Fleming said. "I don't think it's a career-threatening injury, just annoying."