i can only make assumptions, cuz its a concealed RNG thing. But my guess:
Exotic engrams can drop from anything. Almost anything. Could be a final Strike boss, maybe you find one in a random chest out in the world, and maybe (just maybe) a random Dreg you killed drops one. If it's anything like how WoW handles "Legendary" gear (that game's highest level, slot-locked loot), then harder content has higher chances. So theoretically , it's more likely you'll find one in a Raid chest or a raid boss kill than anywhere else. But since those targets are so few in number, its not farmable.
but advice i can give: play public events when you're near em, open every chest you can find no matter where you find it, and kill everything you see, especially elites (which you can be shepherded to by most Adventures, and Lost Sectors are easy, soloable, and short). Kill the biggest baddies you can, turn in what Zone Tokens you get, and just hope then next reward you get is what you want.
There really is no way to "farm" for Exotics outside of breaking down purples for shards to buy whatever Xur in the EDZ has on sale for the week. Hopefully he sells what you specifically want soon.