Short answers, pulled from the story.
According to Genesis 3:24, God entrusted a flaming sword to the cherubim to guard the gates of Paradise after Adam and Eve were expelled. The Hebrew phrase lahat hachereb hammithappeket translates literally as "flame of the whirling sword". Scholars have interpreted it variously as a weapon, lightning, a metaphor, or even bladed chariot wheels.
In Norse mythology, the giant Surtr wields a weapon Snorri Sturluson calls loganda sverð, or "flaming sword", in Gylfaginning 4 of the Prose Edda. Snorri draws on the poem Völuspá 52, which describes Surtr's sword shining with "the sun of the gods of the slain". Some scholars argue the fire describes Surtr's own fiery nature rather than a literal blade.
Dyrnwyn, meaning "White-Hilt", is one of the Thirteen Treasures of the Island of Britain according to the Welsh triads. It belonged to Rhydderch Hael, one of the Three Generous Men of Britain. When drawn by a worthy man, the entire blade blazed with fire, yet every recipient returned it immediately upon learning of this property.
In Vajrayana and Tibetan Buddhism, the flaming sword represents wisdom that pierces ignosis. It appears in the right hand of any Buddha depicted in a thangka painting. Manjushri is the primary example, with his flaming sword marking him as the embodiment of transcendent wisdom.
Kalki is the prophesied tenth and final avatar of Vishnu, destined to appear at the end of the Kali Yuga. He is described in the Puranas as riding a white horse and wielding a fiery sword to end adharma and usher in the Satya Yuga. The Puranas vary in their details about Kalki, with no single account dominating the tradition.
The ancient Gnostic codex On the Origin of the World predicts that the kings under the archons will be "drunken from the flaming sword" during the end times. In this tradition, the sword is neither a guardian nor a purifier but an intoxicant that incapacitates earthly rulers at the moment of cosmic collapse.