I mean

If she is happy what is wrong with that its her choice whither she wants to leave of go btw the duke treat chloe in a considerate alway he gave her chance to go but she did not want to so this does not make him a slave master abd he does not like the idea of slavery even though he knew who she was so yeah

I'd say it's because it was the "best" and "easiest" life she got to know so far. That doesn't make it better. I think the duke is only a temporary owner, because she belonged to that family with the sick little girl before.

And not saying that she should leave him. I’m saying that she should get out of slavery get her papers back and her Freedom. The duke said that he can get her out of slavery which means one of two things he has her papers or he can buy her papers either way in someway or another it still makes him a slave master. If the writer made her a commoner we would not be having this discussion.

If the duke does not like the idea of being a slave master why not let them go saying that if you want you can stay with me or you can leave easy fix

Well, I believe in Chloe's case the concept of slavery when it comes to herself is a bit different. She lived as a slave growing up and she was happy (as one can be), however, the minute the king of the other country found her and released her from her slavery, her life became miserable, since she was thrown into the palace intrigue, sold to a corrupt noble who abused her and was in mortal danger several time during the fall of the country. Then she went back to being a slave, and again, she's living comparatively happier than she did when she wasn't. It's unrealistic, of course, but it's also not too hard to understand that she doesn't mind being a slave when the alternative has not brought her good memories. Chloe has no strong aspirations, which is why she can be happy remaining where she is, as long as her situation doesn't become too difficult to bear. It goes very in line with the concept of slavery as it's seen in Asian history. In ancient China, for instance, servants on a rich house were often under slavery contracts, completely owned by their masters to the point that their master could kill them and nobody would bat an eye. And yet, many peasants and poor people wanted to enter under such contracts, because the alternative sometimes was to starve to death in a slum somewhere, or become a thief or a prostitute. Compared to that, having a roof over their head, with food and clothing provided was a much better alternative, even if it came with the perspective of occasional beatings and the notion of death. Remember "Mankind must first of all eat, drink, have shelter and clothing, before it can pursue politics, science, art and religion." We can discuss it very objectively from the point of view of modern people with their basic needs covered, but in the case of characters living during these eras, it's not as simple.

There are people who found a 'life' so to speak, in slavery, it wasn't the best place nor was it the best life but if their 'owners' were kind and they lived a relatively comfortable and free life then is it not better than being dead or being poor and starving, i think that is the view of Chloe in this case, after all her free life as we have seen was not in any way better than her current life?