The most common image of an angel is essentially a human being with wings. This is not biblical. The Bible often presents angels as appearing as human beings. However, this does not indicate that angels in their essence resemble human beings. Further, the Bible very 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 much is clear, some angels do 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 were having trouble accurately describing the amazing visions they saw of heaven and the angels. As spirit beings, it is unclear as to why the angels would require wings. A spirit being does not need wings in order to fly. The angels are not bound by the laws of the physical universe.
So, do angels have wings? Yes, some angels do have wings. However, we should not limit what the angels can or cannot do based on our limited understanding of the wings some angels possess as described in the Bible.