The most common image of an angel is essentially a human being with wings. This is not biblical. The Bible often presents angels as human beings. However, this does not indicate that angels in their essence resemble human beings. Also, the Bible rarely describes angels as having wings. However, there are definitely two types of angels mentioned in the Bible that have wings: cherubim (Exodus 25:20; Ezekiel 10) and seraphim (Isaiah 6). Cherubim and seraphim are two types of angels, possibly the two highest orders of angels. So this is clear, some angels have wings.
The Bible tells us that angels are spirit beings (Hebrews 1:14). The descriptions of the cherubim in Ezekiel chapter 10 and the seraphim in Isaiah chapter 6 are highly unusual. It is clear that Ezekiel and Isaiah had trouble accurately describing the amazing visions they saw of heaven and angels. As spirit beings, it is not clear why angels would need wings. A spiritual being does not need wings to fly. Angels are not subject to the laws of the physical universe.
So do angels have wings? Yes, some angels have wings. However, we should not limit what angels can or cannot do based on our limited understanding of the wings some angels possess as described in the Bible.