Duminy captained the Proteas in their last T20 series in Australia but was then ruled out of the Test series against the West Indies.
Phangiso, who was injured during the tour of Australia and did not play in the matches there, will be available for the whole series.
Duminy, however, will not play the first two matches but will be available for selection for the third.
The selectors have kept faith with the three players who made their debut in this format in Australia - Reeza Hendricks, Rilee Rossouw and Kagiso Rabada.
"Once again we are resting a number of senior players who are involved across all three formats," said Cricket South Africa (CSA) selection convener, Andrew Hudson.
"This will be the last chance to rest them before we get into World Cup mode with the ODI Series against the West Indies," Hudson added.
