Who were the 'children of the prophets and of the covenant' that Peter was addressing?
Peter addressed Jews as the children of the prophets and of the covenant God made with their fathers in Old Testament days, specifically the Abrahamic covenant. They were Israel, heirs of the promises spoken by the prophets and given through Abraham, not the Church or Gentiles saved by grace.
Les explains that Peter is addressing Jews in this passage. He calls them the children of the prophets and of the covenant God made with their fathers in Old Testament days, saying unto Abraham. Les stresses the Abrahamic covenant, saying everything rests on it. Peter had said that if Israel would repent and be converted, God would send Jesus Christ to fulfill all the covenant promises He made to the nation of Israel. All the prophets from Samuel onward foretold these days—the appearance of their Messiah, His miracles, rejection, crucifixion, resurrection, ascension, and readiness to return. But Les notes there is nothing about the Church yet, and nothing about Gentiles saved by grace.