Rather than Stockholm Syndrome, I think she just chose to look at the positive sides of her present life and finds strength through it. Being a slave is grueling, uncertain, and most of the time I heard, miserable. However, compared to her previous life as a noble, she doesn't get mistreated, and as she said, can freely do the things she loves. Hence, why she feels more grateful and more inclined to being a slave.
It's a matter of survival and which allows her to move more freely. Being appreciative of what she has rather than crying for what she does not have. Chloe's strong in that sense. I think that's amazing of her.
Falling in love with the dude on other hand, idk. Haven't gotten my 2 AM appointment with Dr. Google about it. ¯\_(ツ)_/¯