Satan does have wings, but Satan is not an angel. The misconception that angels routinely have wings may have begun with the assumption that Satan is a fallen angel — which is not what Scripture says.
Ezekiel 28 describes Satan as a "cherub" — a specific order of heavenly being that does indeed have wings (Ezekiel 1, Ezekiel 10). But "cherub" and "angel" are different categories of heavenly beings. The word "angel" (Hebrew: malak; Greek: angelos) means "messenger." Angels appear throughout Scripture in human form without wings.
In every Biblical account where angels appear to humans, they appear in human form — so convincingly so that humans do not immediately recognize them as supernatural (Hebrews 13:2: "Do not neglect to show hospitality to strangers, for by this some have entertained angels without knowing it"). Wings are never mentioned in these appearances.
Beings with wings in Scripture include: Cherubim (Ezekiel 1, 10; Genesis 3:24), Seraphim (Isaiah 6:2), and the "living creatures" of Revelation. These are specific, named orders of heavenly beings — not the general class of beings called "angels."
NO!
Nowhere in Scripture does it say that angels have wings!
Many other created beings have wings, some even have six, but angels do NOT have wings.
The misconception that angels have wings may have originated with the assumption that Satan is an angel.
Satan does have wings, but he is NOT an angel. He is a cherub, a winged being, who ranks above angels and archangels.
Several other types of created beings (spiritual beings, including seraphim) have wings. And various prophets of God have had visions of many different kinds of winged creatures, some holy and some evil.
But the concept of angels having wings is of pagan origin; the belief that angels have wings is folklore, myth, fable, legend, fantasy (imaginary psychological constructs), illusion, or simply a nostalgic tradition inspired by humans.
BEWARE OF DREAMERS:
The stronger the imagination, the more realistic the dreaming result.
And the dreamer with a vivid imagination ends up living in a dream world!
The mind that invents facts, invents ALL facts!
The mind that imagines, imagines EVERYTHING!
The mind that alters, alters EVERYTHING!
And ends up living in the same dream world as the dreamer!
Genesis 28:12 - JACOB'S LADDER - "And he dreamed, and behold, a ladder was set up on the earth, and its top reached to heaven; and behold, the angels of God were ascending and descending on it."
John 1:51 - And he said to him, "Truly, truly, I say to you, you will see heaven opened, and the angels of God ascending and descending on the Son of Man."
Revelation 8:13; and 14:6, 8, 9 - Reference is made to angels "flying in the midst of heaven" without any mention of those angels having wings. Angels DO NOT NEED wings to fly. Angels, as spiritual beings, are not subject to physical laws, gravity, etc.
Because there is NO indication anywhere in the Bible that angels have wings.
The original Hebrew and Greek manuscripts of the Christian Bible have NO mention of angels having wings.
Any modern translation or paraphrase of the Bible that says angels DO have wings is a mistranslation and is incorrect.
Everyone has a right to their own traditions, customs, beliefs, opinions, and points of view (POV), along with their own Roman Catholic folklore, pagan myths, fables, fantasies, and illusions.
But they are NOT entitled to their own facts!
The following are Biblical FACTS!
If YOUR copy of the Bible says that angels DO! If you have wings, you need to get rid of that bad, misleading, and unreliable translation and get a New American Standard (NASB) version of the Bible.
The NASB is, technically, the most reliable and accurate translation from the original Hebrew and Greek manuscripts into modern American English. A British English speaker would probably be more comfortable with the Authorized King James Version (revised 1881-85).