Slavery never allowed by God.

[Link]

Salam

(1) Slaves of God exist and we are his servants, other types are false.
(2) The malakat aymanihim in most places refers to muta.
(3) "Your servants" has a similar meaning to "your disbelievers" or "their Prophet", it doesn't denote ownership but rather "the servants (of God) from you" type meaning.
(4) Captives does not mean slaves.
(5) Quran shows to ransom or free captives by grace till furry of war terminates, meaning, they should be freed at that point (when war is over).

 

[Link]

Salam

The absence of Hajar and the jealousy story in the Quran speaks volumes in itself that Ibrahim (a) didn't have a slave.

 

[Link]

Salam

Freeing a neck should be seen in context of freeing captives or slaves. However, it doesn't imply that it is not a wrong thing to have slaves.