I’ve heard this phrase being thrown around sometimes on other game tables. Apparently, it describes a straight line of melee combatants on a grid, alternating between members of two opposing groups. This only occurs if the Flanking Variant Rule are used. Under these circumstances, the Conga Line of Death makes sense from a mechanical standpoint, as every melee combatant wants to get advantage on their attack rolls. If this rule were in place, player characters as well as NPCs would understand the in-universe ramifications and probably try to get into a superior position every time, leading to the aforementioned Conga Line of Death.
Now my question is: How can I, as DM, avoid the Conga Line of Death occurring when implementing some form of flanking rule?
The obvious answer would be: “Don’t use the Flanking Variant Rule”. Well, I for one like to grant some form of advantage, when two combatants gang up on their opponent. And it kind of makes sense, that it is easier to hit somebody who has to avoid the attacks of two enemies. So I want to keep Flanking in my game, but like to prevent the Conga Line of Death.
Best Answer
Negation of Advantage
At our table we use the Variant Flanking rules, however we noticed the same problem as yourself, and added the corollary that you cannot gain Advantage from a Flank if you yourself are being Flanked. The thematic justification was that you are busy trying to cover your own back and can't put all of your attention onto exploiting the enemy's defensive gaps.
This is justified mechanically under the rules for gaining advantage and disadvantage:
It led to players holding formations, covering each others back and using the terrain more to their advantage, using low walls and pillars to block enemy movement into the now more limited flanking positions.
It may be worth noting that at our table, while we do not grant Advantage to a Flanked Flanker, we don't actually class them as having received disadvantage for purposes of "multiple cases of advantage and disadvantage do not stack". Effectively meaning that any other source of gaining Advantage would still be enough to give the player an edge. This was done as else spells such as Darkness and Guiding Bolt lost a fair amount of utility. YMMV on this however.