You have to have these consumables:
Black Wax Idol:
The way these items work is that for every enemy you kill you get roughly 3-6 destiny glimmer each on average, but if you can string together multiple kills (they work on a timer, like double kills, triple kills, etc.) the amount of destiny glimmer you get for each successive kill increases. So for the first kill in a streak you might get maybe 4 destiny glimmer, then for the second kill you’ll get 8, then 12 and it keeps increasing until you go more than about 4 or 5 seconds without a kill, then it resets.
Best place to use them is at Skywatch in free roam since there are about 4 different enemy spawns very close to each other that spawn enemies relatively frequently.
You’ll also want to use both items at the same time because one item only gives you destiny glimmer for killing Hive enemies and the other for Fallen enemies, and each of the spawns in that location only spawn one type of enemy. It’s really hard to keep the kill streak going fighting only one type of enemy, since you will end up waiting for them to spawn when you could keep it going by fighting the other enemies.
The other good thing about this area is that there will be public events that spawn a ton of enemies, one I believe is to defend the Warsat, and the other isn’t an actual public event (no idea what it is called) but every once in a while for about 5 or 10 minutes there will be massive waves of Hive and Fallen that spawn on either side of the area, fighting each other. There will be a lot of high ranking enemies too. Towards the end you will probably die a lot even if you have other Guardians helping you.
Using those three consumable items that I had I was able to get over 2000 destiny glimmer (and tons of loot) in about 20 minutes (up to 7653 from 5398):
The highest I got my chain to go was 173 glimmer per kill (ended cause I was killed), during the event with the huge waves of enemies: