This question refers to two verses:
For if God did not spare angels when they sinned, but cast them into hell and committed them to chains of gloomy darkness to be kept until the judgment. (2 Peter 2:4)
And the angels who did not stay within their own position of authority, but left their proper dwelling, he has kept in eternal chains under gloomy darkness until the judgment of the great day. (Jude 6)
These two passages relate to the Enoch myth of 200 angels which fell in the days of Noah and were the cause of the flood. The myth was based on a misreading of Genesis 6:1-4. The timeline of this story can be set out as follows:
- Gen.6:2 — sons of God and daughters of men
- Jewish readings of Gen.6 vary.
- 2ndC BC — Enoch myth begins to circulate in Judaism, probably originally as political comment on corruption
- 1stC BC — Enoch myths grow in popularity, many versions — 1 Enoch, Jubilees, etc.
- 1stC AD — several versions of Enoch myths — 1 Enoch, Book of the Giants – in use at Qumran.
- Rabbi Shamai against the reading of Gen.6 as angels
- Luke 20 – Christ teaches that angels do not marry, and that “sons of God” are men in the resurrection.
- Col 2:18 — Paul warns about “religion of angels”
- Titus 1:14 — Paul warns about “Jewish myths”
- 1 Peter — indirect allusions to a problem, “spirits in prison, who sinned in the days of Noah”
- 2 Peter — direct dealing with the problem as a “myth”, several quotes and allusions to the text of 1 Enoch.
- Jude — reminding the words of Peter (in the past tense, indicating that he was dead) and direct citation from 1En.1:9 in Jude 14
- Trypho the Jew and Justin Martyr debate Gen.6 (Trypho being against the angel version, Justin for).
- 2ndC — Enoch literature circulates widely in Early Christianity, being the dominant story for the origin of the devil.
- 3rdC — Enoch myth begins to be replaced by the Lucifer story drawn from Isaiah 14.
- 4thC — 1Enoch listed as a banned book. Survives in Ethiopia and Black Sea.
- 19thC — Tischendorf, R.H. Charles and M.R. James work on recovering Greek and Coptic versions of 1Enoch and other Jewish myths
- It is difficult to deny that Jude 14 is a quote of 1En.1:9, though some argue 1En.1:9 is a quote from Jude 14.
- 1948 — copies of 1Enoch predating Jude discovered at Qumran
- 1968 — Geza Vermes publishes the Aramaic 1Enoch in English
- 1990s — copyleft versions of 1Enoch in Charles’ and James’ translations circulate widely on the Internet
That’s the background. Now to look at the text the question is not whether Peter and Jude (and indeed Christ and Paul) were aware of the Enoch legends, that is beyond dispute. The question is how they regard them?
This is best set out as a commentary:
Analysis of 2 Peter 2:
2 Peter 2:1 But false prophets also arose among the people, just as there will be false teachers among you, who will secretly bring in destructive heresies, even denying the Master who bought them, bringing upon themselves swift destruction. 2 And many will follow their sensuality, and because of them the way of truth will be blasphemed. 3 And in their greed they will exploit you with false words. Their condemnation from long ago is not idle, and their destruction is not asleep.
Note the three red-light warnings before Peter introduces the Enochic material (a) there will be false teachers among you, (b) who will secretly bring in destructive heresies… (c) And in their greed they will exploit you with false words. These are not a vote of confidence in what follows next, but a health warning.
4 For if God did not spare angels when they sinned, but cast them into hell  and committed them to chains  of gloomy darkness to be kept until the judgment; 5 if he did not spare the ancient world, but preserved Noah, a herald of righteousness, with seven others, when he brought a flood upon the world of the ungodly; 6 if by turning the cities of Sodom and Gomorrah to ashes he condemned them to extinction, making them an example of what is going to happen to the ungodly;  7 and if he rescued righteous Lot, greatly distressed by the sensual conduct of the wicked 8 (for as that righteous man lived among them day after day, he was tormenting his righteous soul over their lawless deeds that he saw and heard); 9 then the Lord knows how to rescue the godly from trials,  and to keep the unrighteous under punishment until the day of judgment, 10 and especially those who indulge in the lust of defiling passion and despise authority.
Note, “if”. Peter’s argument is that “if” the myth is true and the 200 angels were chained by Raphael in Tartarus, then they cannot harm anyone. The logic of this holds today. If (hypothetical) people believe angels fell from heaven then they should also accept the story that they are chained.
Bold and willful, they do not tremble as they blaspheme the glorious ones, 11 whereas angels, though greater in might and power, do not pronounce a blasphemous judgment against them before the Lord. 12 But these, like irrational animals, creatures of instinct, born to be caught and destroyed, blaspheming about matters of which they are ignorant, will also be destroyed in their destruction, 13 suffering wrong as the wage for their wrongdoing. They count it pleasure to revel in the daytime. They are blots and blemishes, reveling in their deceptions,  while they feast with you. 14 They have eyes full of adultery, insatiable for sin. They entice unsteady souls. They have hearts trained in greed. Accursed children! 15 Forsaking the right way, they have gone astray. They have followed the way of Balaam, the son of Beor, who loved gain from wrongdoing, 16 but was rebuked for his own transgression; a speechless donkey spoke with human voice and restrained the prophet’s madness.
Blaspheming glories (Greek doxai, a term for the heavenly court) means that the blasphemy is not true. So if those teachers charge angels with sinning, and this charge is blasphemy (according to Peter), then it follows that the charge is false.
17 These are waterless springs and mists driven by a storm. For them the gloom of utter darkness has been reserved. 18 For, speaking loud boasts of folly, they entice by sensual passions of the flesh those who are barely escaping from those who live in error. 19 They promise them freedom, but they themselves are slaves  of corruption. For whatever overcomes a person, to that he is enslaved. 20 For if, after they have escaped the defilements of the world through the knowledge of our Lord and Savior Jesus Christ, they are again entangled in them and overcome, the last state has become worse for them than the first. 21 For it would have been better for them never to have known the way of righteousness than after knowing it to turn back from the holy commandment delivered to them. 22 What the true proverb says has happened to them: “The dog returns to its own vomit, and the sow, after washing herself, returns to wallow in the mire.”
A series of quotes and illusions taken from 1Enoch to false teachers – but in this case it is not those teachers of the days of the flood who were influenced by the fallen angels, it is the teachers of Peter’s day who are “waterless springs” etc.
Two additional points from Jude.
Judgment on False Teachers
Jude 3 Beloved, although I was very eager to write to you about our common salvation, I found it necessary to write appealing to you to contend for the faith that was once for all delivered to the saints. 4 For certain people have crept in unnoticed who long ago were designated for this condemnation, ungodly people, who pervert the grace of our God into sensuality and deny our only Master and Lord, Jesus Christ.
Again the same point as Peter — the problem is not fallen angels, but teachers among you.
5 Now I want to remind you, although you once fully knew it, that Jesus, who saved  a people out of the land of Egypt, afterward destroyed those who did not believe. 6 And the angels who did not stay within their own position of authority, but left their proper dwelling, he has kept in eternal chains under gloomy darkness until the judgment of the great day— 7 just as Sodom and Gomorrah and the surrounding cities, which likewise indulged in sexual immorality and pursued unnatural desire,  serve as an example by undergoing a punishment of eternal fire.
Again the same point as Peter, the angels of 1Enoch are chained, not roaming free.
8 Yet in like manner these people also, relying on their dreams, defile the flesh, reject authority, and blaspheme the glorious ones.
Again, if they blaspheme angels — what they say cannot be true, can it?
9 But when the archangel Michael, contending with the devil, was disputing about the body of Moses, he did not presume to pronounce a blasphemous judgment, but said, “The Lord rebuke you.” 10 But these people blaspheme all that they do not understand, and they are destroyed by all that they, like unreasoning animals, understand instinctively. 11 Woe to them! For they walked in the way of Cain and abandoned themselves for the sake of gain to Balaam’s error and perished in Korah’s rebellion. 12 These are hidden reefs  at your love feasts, as they feast with you without fear, shepherds feeding themselves; waterless clouds, swept along by winds; fruitless trees in late autumn, twice dead, uprooted; 13 wild waves of the sea, casting up the foam of their own shame; wandering stars, for whom the gloom of utter darkness has been reserved forever.
The context is that in 1Enoch Michael accuses the 200 angels, but in Zechariah 3 the angel of the Lord did no such thing.
14 It was also about these (incorrect, Greek says “to these“) that Enoch, the seventh from Adam, prophesied, saying, “Behold, the Lord comes with ten thousands of his holy ones, 15 to execute judgment on all and to convict all the ungodly of all their deeds of ungodliness that they have committed in such an ungodly way, and of all the harsh things that ungodly sinners have spoken against him.” 16 These are grumblers, malcontents, following their own sinful desires; they are loud-mouthed boasters, showing favoritism to gain advantage.
The so-called quote from “Enoch, the seventh from Adam” (itself a quote from 1En) is not from the real Enoch at all but from Moses:
De.33:2 He said, “The Lord came from Sinai and dawned from Seir upon us; he shone forth from Mount Paran; he came from the ten thousands of holy ones, with flaming fire at his right hand.
Jude recognised what modern scholars also recognise, that 1En1:9 is a midrash of De.33:2 (see Nickelsburg). Jude therefore is saying 1Enoch (the book) prophesies “to these” (the false teachers) the words of Moses (in which angels condemn men, not men condemn angels).