How does one obtain the "black" camo in BF3?

Solution 1:

Spec Ops camo is unlocked at level 42.

It doesn't have the special properties you listed (that being harder to spot for your teammates) it does however have the special property of making you harder to see if your enemy is using an IRNV scope.

While wearing it, the black parts of your camo (not your gun or the ammo pouches etc.) will not show any heat through an IRNV scope.