What incident is Peter referring to when he mentions the angels who were not spared?

It is not clear exactly to what event Peter is referring, though it appears to be the same event as the one which Jude had in mind (Jude 1:6). The apostasy of the angels is not found anywhere in the Old Testament. The idea of a pre-historic angelic fall, however, is present in Revelation (see Revelation 9:1–21, Revelation 12:1–17 and Revelation 20:1–15) and Peter could thus be alluding to how Satan and his followers rose up against God.  (One problem with this interpretation is the fact that Satan and his fallen angels are said to be wondering around the earth (1 Peter 5:8; Job 1:7; Revelation 12:9) rather than being kept in chains).¹ Given the challenges with this interpretation, most commentators understand that Peter is indirectly referring to the events of Genesis 6:1–4. In Jewish interpretative tradition, the sons of God were understood as being angels (see 1 Enoch 6-12) and their sin was having sexual relations with human women.^2,3,4,5 A final possibility is that Peter was referring to messengers of the covenant who were operating before the flood, the godly line of Seth. These were the sons of God mentioned in Genesis 6:1–4 and though the NIV suggests that Peter talks about angels, the Greek word for angel can also be translated as messenger (see Matthew 11:10; Luke 7:24, Luke 7:27; Luke 9:52; Mark 1:2; James 2:25). When these messengers sinned by marrying women outside the covenant or godly line, they were judged in the flood and have been kept also for the day of final judgment.⁶

Whatever event Peter had in mind, he is emphasizing the fact that those who sinned are kept for judgment and they will not escape God’s wrath. His main emphasis is thus the certainty of judgment and not the reason for judgment.⁷ No mercy was nor will be shown to these angels or messengers (see Deuteronomy 7:16; Deuteronomy 13:8; Deuteronomy 19:13; 1 Samuel 15:3; Psalm 78:50; Jeremiah 13:14; Ezekiel 5:11; Ezekiel 7:4; Romans 11:21).