Just theoretically here...
Lore wise beast men (while they are good) would never have the slaves because they are locked into good alignment. In theory they would only get an option to have slaves once they cross into bad, but at that time they wouldn't be allowed to go to Arboreus anymore. So Arboreus as a planet would have no slavery.
Syndesia, and Tartaros would have possibility for slavery. Syndesia is a constant battle between good and evil, so if there was an evil city with slavery, once this city was taken and new city government would turn it into good, slaves that are there would be freed. So Syndesia would have changeable situation depending on who owns which city and how he rules it.
Tartaros as FFA would have no rules, but existing slaves would get stolen by one player from other player, and they would change hands same as any other goods. So for that reason, you would be able to have slaves, but you wouldn't have any security about how long you will get to keep them.