Most of my historical reading is in the ancient world, where slaves are often involved in conflicts in the sense that one side or the other promises them freedom for fighting with them: this seems essentially transactional rather than appealing to national feeling. I'd guess that slaves in the Roman Empire who had powerful/prestigious roles and material comforts might have felt part of Roman civilisation and identified with it.
But did American politicians or slave-owners expect chattel slaves to be stirred by the Star-Spangled Banner or to identify as part of America, or similar for other more recent slave-owning countries ? Would they have even wanted them to, or would identity with the nation (especially one 'founded on liberty') be too revolutionary?
I would encourage you to read u/sowser's incredible 5-part description of how we study slavery. It goes into a lot more than what you are asking for here about modern concepts of freedom and slavery, but here's one part that might help answer or at least frame some thinking around your question:
[19th century Serfdom] is in sharp contrast to the people taken into the transatlantic slave system and their descendants. Enslaved people did not have an identity of their own in law or culture; the system of transatlantic slavery was predicated on the absolute degradation of humanity. Enslaved people were very much made objects of and within the law of the territories in which they were held in bondage. They did not enjoy any of the basic protections of cultural or political frameworks that serfs could and often did. They were literally the property of their masters and had value for that reason as well, not simply because of their capacity for labour. The distinctive characteristic of slavery is that it is utterly dehumanising in every single way. The enslaved person is excluded from any legitimised participation in the society in which they labour; if they do participate it is at the whim of the people who claim to own them.