Have you done the Strela and RPG? They're the manual fire ones that don't lock on, they're 10x harder than the JOKR and the other one.

In all honesty it just takes time. If they bring back the 'Drop Zone' playlist, then play that (dozens of supply drops per game) - I was shooting down like 4/5 killstreaks a game, but they took that playlist off last week.

General tips, play either Ground War or the smaller maps with longer game times (e.g. Domination, Hardpoint) so people get killstreaks more often. Stand at the back of the map on GW and wait for them. If you run out of rockets, blow yourself up with a thermite/c4/grenade to respawn. Your K/D ratio will take a beating but that's what it takes for Damascus.