How many illegal guns are in the US?

None. When made, 99.9% are legal, no matter where made. Just because it's against the law for YOU to own it doesn't make the weapon illegal.

Technically the above is correct however as guns are not required to be registered in all states it is impossible to say how many are owned legally. Guns that are owned illegally are obviously not registered so there is no way to know how many there are.