The Bible does not record angels having wings at any point, but this is a popular depiction of angels. Do any Christian groups teach that angels do have wings, in extra-biblical materials? Where does the idea come from?
The Bible actually does indicate that angels have wings, as both cherubim and seraphim are angels.
It is also assumed that the four living creatures are angelic beings, since it's hard to imagine what else they could be:
And the four living creatures, each of them with six wings, are full of eyes all around and within, and day and night they never cease to say, "Holy, holy, holy, is the Lord God Almighty, who was and is and is to come!" Revelation 4:8