The Bible does not tell us much about angels or demons. What we do know, is that Satan and his demons will be totally destroyed one day, not burn in hell forever as some teach, but be totally burnt up until ashes. And reincarnation is a pagan belief, which is not mentioned in the Bible and has no place in Christianity, so definitely would not apply to angels or demons either. Look at what the Bible has to say.

Matthew 25:41   “Then He will also say to those on the left hand, ‘Depart from Me, you cursed, into the everlasting fire prepared for the devil and his angels’”.

Jude 1:6   And the angels who did not keep their proper domain, but left their own abode, He has reserved in everlasting chains under darkness for the judgment of the great day.

2 Peter 2:4   For if God did not spare the angels who sinned, but cast them down to hell and delivered them into chains of darkness, to be reserved for judgment.

Ezekiel 28     ¹⁴ “You were the anointed cherub who covers; I established you; you were on the holy mountain of God; you walked back and forth in the midst of fiery stones.
¹⁵ You were perfect in your ways from the day you were created, till iniquity was found in you.

¹⁸ You defiled your sanctuaries by the multitude of your iniquities, by the iniquity of your trading; therefore I brought fire from your midst; it devoured you, and I turned you to ashes upon the earth in the sight of all who saw you. ¹⁹ All who knew you among the peoples are astonished at you; you have become a horror, and shall be no more forever.”

Malachi 4     “For behold, the day is coming, burning like an oven, and all the proud, yes, all who do wickedly will be stubble. And the day which is coming shall burn them up,”
Says the Lord of hosts, “That will leave them neither root nor branch.
² But to you who fear My name the Sun of Righteousness shall arise with healing in His wings; and you shall go out and grow fat like stall-fed calves.
³ You shall trample the wicked, for they shall be ashes under the soles of your feet on the day that I do this,” says the Lord of hosts.

Psalm 37     ⁹ For evildoers shall be cut off; but those who wait on the Lord, they shall inherit the earth.  ¹⁰ For yet a little while and the wicked shall be no more; indeed, you will look carefully for his place, but it shall be no more.

²⁰ But the wicked shall perish; and the enemies of the Lord, like the splendor of the meadows, shall vanish.  Into smoke they shall vanish away.

From the above passages you can see that it never talks about angels or demons dying, but that the fallen angels are being kept for the final judgment, after which they, together with Satan and the wicked, will perish. As we can see, perish means being totally destroyed by fire, until only ashes remain.

I trust that this makes sense to you. God bless!