I cannot give you more scripture background, since this is the only place in scripture that contains the phrase "flaming sword."
However, "Cheribums" are well understood in scripture to be the special powerful angels who guard the very throne of God, and it is well within logic to expect a cheribum to wield a sword worthy of a cheribum:
Psa 99:1 The LORD reigneth; let the people tremble: he sitteth between the cherubims; let the earth be moved.
2Ki 19:15 And Hezekiah prayed before the LORD, and said, O LORD God of Israel, which dwellest between the cherubims, thou art the God, even thou alone, of all the kingdoms of the earth; thou hast made heaven and earth.
1Ch 13:6 And David went up, and all Israel, to Baalah, that is, to Kirjathjearim, which belonged to Judah, to bring up thence the ark of God the LORD, that dwelleth between the cherubims, whose name is called on it.
Isa 37:16 O LORD of hosts, God of Israel, that dwellest between the cherubims, thou art the God, even thou alone, of all the kingdoms of the earth: thou hast made heaven and earth.
Therefore, God himself made this no small assignment by whom he chose to do the work of bearing this flaming sword. I like John Wesley's commentary on this scripture:
"Gen 3:24 God drove him out - This signified the exclusion of him and his guilty race from that communion with God which was the bliss and glory of paradise. But whether did he send him when he turned him out of Eden? He might justly have chased him out of the world, Job_18:18, but he only chased him out of the garden: he might justly have cast him down to hell, as the angels that sinned were, when they were shut out from the heavenly paradise, 2Pe_2:4, but man was only sent to till the ground out of which he was taken. He was only sent to a place of toil, not to a place of torment. He was sent to the ground, not to the grave; to the work - house, not to the dungeon, not to the prison - house; to hold the plough, not to drag the chain: his tilling the ground would be recompensed by his eating its fruits; and his converse with the earth, whence he was taken, was improveable to good purposes, to keep him humble, and to mind him of his latter end. Observe then, That though our first parents were excluded from the privileges of their state of innocency, yet they were not abandoned to despair; God's thoughts of love designing them for a second state of probation upon new terms. And he placed at the east of the garden of Eden, a detachment of cherubim, armed with a DREADFUL AND IRRESISTIBLE POWER, represented by flaming swords which turned every way, on that side the garden which lay next to the place whither Adam was sent, to keep the way that led to the tree of life."
John the Baptist
Answered By: † John The Baptist † - 11/18/2009