How does the 'Lets Dance' bounty work?

If you have the first dlc the best location is the "Fist of Crota" mission on Earth — after the Sword bearer spawns you can pick up the sword and run to the next area where three packs of thralls attack — plenty enough for a quick melee chain.

Source: Just did it myself after trying several other farming spots.

As far as I have seen from youtube and such most people have no longer than 3 seconds between each consecutive kill. It can be achieved whilst in arc blade aswell.

As for time between kills? It's a rough estimate as only seen people achieve with kills in a 3 second window consecutively but to narrow down a hard factual number would be difficult I imagine unless Bungie suddenly announce it or some serious testing! :P