The answer to this question is, like the history of our country, quite complex. Slavery existed in places like the Eastern Woodlands long before contact, but the nature of slavery and enslavement, as well as the development of justification for enslavement based on race, changed significantly as the country moved from a series of small footholds on the Atlantic coast, to a confederation of thirteen colonies, to U.S. hegemony east of the Mississippi River.
Slavery existed in various forms in different Native American communities before contact. Throughout the Eastern Woodlands raiding for captives formed an integral aspect of warfare, and captive exchange was a crucial aspect of forging peace between communities. Practices varied, but captives could be adopted into their new nation, rise to prominence, and their children could inherit a non-stigmitized status as a full member of the nation. Rushforth tends to present a less benign view of captivity in the Great Lakes region, where refusal to assimilate brought worse status and treatment, but those who adapted to their new state could experience a large degree of freedom.
Practically, small parties of warriors would raid neighboring nations for slaves. These captives would be ritually adopted, often given the name of a beloved recently deceased relative, and placed into families. Again, practices varied, but this form of slave raiding could be seen as an attempt to bolster population size, and for nations like the Haudenosaunee/Iroquois, allow the community to ritually heal during a period of mourning.
The nature of Native American slavery changed dramatically in the seventeenth century. In the Southeast Carolina slave traders transformed captives into goods that could be bought and sold. Instead of raiding neighbors in the cyclic pattern of small scale conflicts, larger parties set out on long distance raids with the sole intent to capture enemies for sale, not adoption. These raids were used with brutal effectiveness in Florida, where Carolina sought to undermine the Spanish mission system by enslaving their allied Native American population.
Accurate numbers will be hard to come by for this period, but Gallay believes 4,000 Florida Indians were captured and enslaved between 1704 and 1706. In 1708 the Governor of Florida, Francisco de Corcoles y Martinez estimated ten to twelve thousand Indians were taken from Florida. Father Joseph Bullones reported that four-fifths of the Christian Indians remaining in Florida after 1704 were killed or enslaved. The scale of raiding was so catastrophic that refugees fled south, hoping for transport and safe haven in Cuba. A ship captain carried 270 Florida refugees to Cuba in 1711, and said he left 2,000 Christian Indians and 6,000 more seeking baptism when he departed the Florida Keys. Gallay's very conservative estimate for the total number of people enslaved, not counting those who died in the associated warfare and displacement, in Florida alone is 15,000-20,000. The peninsula was practically depopulated of Indians by the early eighteenth century. If we go further out to include the greater Southeast, Gallay's very conservative numbers suggest 30,000-50,000 Amerindians were captured directly by the British, or by allied Native Americans for sale to the British, and enslaved before 1715. Carolina exported more slaves than it imported before 1715. This number does not include those who died as a result of hostilities related to the slave trade, those displaced by the endemic warfare, or those who died as a result of infection and malnutrition common to refugee populations the world over.
All this to say, that before the early 1700s slavery in North America very much depended on Native Americans as slavers, and as slaves. Depending on need, and expediency, there were few limits on adoption for Europeans, Africans, or other Native Americans. By some estimates more than half of the population of Iroquoia were transplants during the height of the Beaver Wars. However, with the commercialization of the slave trade, victims of slaving raids could just as easily be bound for a short, painful life toiling on plantations in the Caribbean, and Settlement Indians found one of the few ways to make a living after losing their land was cashing in on hefty bounties for returning escaped slaves, both African and Indian.
After exhausting the Native American supply, the English colonies began importing larger numbers of African slaves. In places like Massachusetts and Virginia the legal justification for Indian enslavement was modified to form a race-based chattel slavery model for the growing colonies. The number of African slaves jumped dramatically, as did the dependence on fertile land beyond the frontier.
To pay for a costly revolution, and avoid a class war between landed gentry and poor newly-arrived immigrants, the new United States required cheap land across the Appalachian mountains. The U.S. enacted an Indian Policy that was essentially a land policy. Native Americans would be offered the chance to sell their lands in exchange for money and assistance becoming civilized (adopt agriculture, give up hunting grounds, learn to read, and essentially abandon Indian identity). Those who refused faced total war, designed to exterminate and cleanse the land of Indian presence to allow for white settlers.
For those like the Cherokee and Creeks, adapting to the U.S. form of race-based chattel slavery was part of becoming "civilized". Between the late 1700s and the Civil War an estimated ten thousand African slaves toiled in the tobacco and cotton fields for their Native American owners. James Vann, a Cherokee plantation owner in Georgia, owned more than a hundred slaves, making him one of the elite southern planters. According to Calloway, he treated his slaves as harshly as any white owner. The 1835 Cherokee Census counted 2,637 heads of households, 16,542 Cherokees, and 1,592 African American slaves. Despite all their attempts at assimilation, a growing United States could not abide Native American neighbors. In 1838 federal troops enforcing the Treaty of New Echota rounded up Cherokees, and their slaves, placed them in internment camps, then forced them to march to their new homes across the Mississippi. Roughly a quarter would die on the Trail of Tears to Oklahoma.
Whereas previous notions of race and identity were significantly more fluid, and adoption of outsiders more common, by the early nineteenth century the predominant ideas of racial hierarchy strained old kinship patterns. Intermarriage still existed between Native Americans, whites, and Africans as it had since the beginning of the colonies, but life in a society with strict racial hierarchies meant by the 1800s Native American owners east of the Mississippi were much more likely to buy slaves to make a profit, not replace loved ones.
Sources:
Colin Calloway The Indian World of George Washington: The First President, the First Americans, and the Birth of the Nation
Colin Calloway First Peoples: A Documentary Survey of American Indian History
Alan Gallay The Indian Slave Trade: The Rise of the English Empire in the American South, 1670-1717
Margaret Ellen Newell Brethren by Nature: New England Indians, Colonists, and the Origins of American Slavery
Theda Perdue Cherokee Removal: A Brief History with Documents
Brett Rushforth Bonds of Alliance: Indigenous and African Slaveries in New France