Hebrews 1:7 (KJV)
"And of the angels he saith, Who maketh his angels spirits, and his ministers a flame of fire."
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Bibleref.com answers your question quite well, in my opinion. I doubt I could answer your question any better than they.
This verse continues a string of proofs from the Old Testament, showing that Jesus is more than simply an angelic being. In fact, according to these Scriptures, He is unique in His power and authority, and equal to God.
Verse 7 has to be read along with verses 8 and 9 to fully grasp the point. The writer of Hebrews is making a distinction between angels, who God treats as servants, and the Messiah, who God treats as a ruler.
In this case, the reference is to Psalm 104:4. Psalm 104 celebrates God's creative power and His blessing on all He has created. Psalm 104:4 specifically refers to God directing the actions of His "messengers," which is from the Hebrew word malākāy, the same term translated as "angels." The point being made is that angels are beings commanded by God as servants. They are not invested with authority. Instead, they are used in much the same way as other parts of creation.
This verse also suggests that God sometimes delivers His message, via His angels, using them through the natural world. Some see this as part of the contrast Hebrews is presenting, as well. While angels, per Psalm 104:4, have a flexible nature, sometimes appearing as flames or wind, the upcoming Scriptures will show that Christ has an eternal and unchanging nature—further proof that He is God.
Verses 8 and 9 will contrast the servant status of angels with the ruling status of Jesus Christ.
A good follow-up question would be "In what ways (or in what instances) did God use his servant-angels as a flame (or flames) of fire? A couple hints: 1) Genesis 3:24; 2) Deuteronomy 33:2ff.
Another thoughtful article on the theme of angels' roles in God's work is found here. To whet your appetite, I quote the following paragraphs from that article.
What are the roles of the various parties in the giving of the law? Perhaps, before reading this article, you thought: God to Moses to the people. But there is a fourth party too, making it: God to the angels to Moses to the people. In fact, a fifth party is also involved: Christ (Acts 7:38, cf. v. 30), "the messenger of the covenant" (Mal. 3:1). This is the complete chain of revelation: the Triune God (the sovereign Lord and author of the law) to Christ (the pre-incarnate Word) to the angels (who were present to order and speak the law) to Moses (the Old Testament mediator) to the people of God.
This is analogous to the book of Revelation. Revelation 1:1 teaches this chain of revelation: God to Christ to an angel (not angels) to John (not Moses) to the people of God. A close reading of Daniel 8-12 and Zechariah 1-6 will reveal something similar regarding God’s revelation given through these two prophets.
While the overall point that Hebrews 1 is making is clear enough, it does not help that almost all English versions have mistranslated verse 1:7, because they ignored the fact that the author is quoting the literal LXX translation of the Hebrew text. Admittedly the Greek text has an unusual word order in 1:7 so that it is not clear what is subject and what is object, but that is because the LXX followed the word order of the Hebrew text and Hebrews 1:7 quoted the LXX (Ps 103:4) without changing the word order.
I have written at some length about this 10 years ago here: Does God let ministers go up in flames.
It can also be found here: Does God set his servants on fire
Briefly stated, Psalm 104:4 says:
You use the winds as your messengers and flashes of lightning as your servants. (GNB)
There are several examples in the OT where God fights for his people by using storms to help them against their enemies, for instance, heavy mud can cause the chariot wheels to get stuck (Exo 14:25; Judges 5:19-21).
If we compare the Greek text as found in the LXX with the Greek in Heb 1:7 we find:
ὁ ποιῶν τοὺς ἀγγέλους αὐτοῦ πνεύματα καὶ τοὺς λειτουργοὺς αὐτοῦ πῦρ φλέγον. (Ps 103:4 LXX)
Ὁ ποιῶν τοὺς ἀγγέλους αὐτοῦ πνεύματα καὶ τοὺς λειτουργοὺς αὐτοῦ πυρὸς φλόγα, (Heb 1:7)
The author of Hebrews clearly intended the same meaning as found in the Hebrew text of Psalm 104. The point in Hebrews 1:7 is that the angels are not up there at the same level as God and Jesus (and not to be worshiped). Even the thunderstorm and lightning are used by God as his “angels”, i.e. messengers. “Jesus is far above the angels” is the major theme of this passage in Hebrews.
Almost the only version which I think got it right is the New Jerusalem Bible:
NJB: appointing the winds his messengers and flames of fire his servants. (Heb 1:7)
NJB: appointing the winds your messengers, flames of fire your servants. (Ps 104:4)
Please see my answer to a related question.
The short answer is that this is simply an example of the corruption introduced in the scriptural documents in their transmission from Hebrew to the NT via the foibles and plots of the Hellenists that produced the "LXX".