These are bought in the borg refinery. You can buy 100 Regular Directives every day if you have a tier 9 Vi’dar (unfortunately lower tiers can only get 9 directives a day and should not be bought). Then, when you defeat these armadas, you can exchange the loot for a chest which will get you 100 Rare Directives. When you defeat rare armadas, you can exchange the loot for a chest which will get you 200 Epic Directives. Assuming the amount of loot is similar to Dominion Solo Armadas, you should be able to get a regular chest ~every other day, a rare every ~sixth day, and an epic every ~eighteenth.

These chests will also give you the Commander XP you need to upgrade your admirals — Kirk, Spock and Locutus, as well as Borg Officer Shards.