Did slaves ever seek refuge with native americans?

This is a yes and no question. It is important to remember here that indigenous American tribes did not have a homogenous response to European and later American settlement. Some tribes, notably the Five Civilized Tribes in the southeastern United States (Cherokee, Choctaw, Chickasaw, Creek, and Seminole) adopted American style slavery as a mechanism for assimilation. Michael F. Doran sums this up nicely, noting that slavery was “transferred almost intact to the Indian society from Southerners.” He expands on this, writing:

Negro slaves constituted the single most numerous minority group among the Five Civilized Tribes from an early date, and by 1860 outnumbered alien whites in the Indian Territory by a ratio of more than three to one. The several thousand slaves at that date, and presumably earlier as well, were only owned by a small group. According to the manuscript census schedules, not quite 2.5% of tribal citizens and about 5% of alien white residents actually owned slaves. The slaveholding element constituted a tiny elite in the Indian society, but evidently one with disproportionate economic and political power. Contemporary reports on Indian life inevitably associated the families possessing slaves specifically with "easy" or "better" circumstances, in contrast with the mass of the populace who lived in grinding (but seemingly unconcerned) poverty. In the context of the slave-owning citizen families, literary evidence states that the wealthy parties were mixed both in blood and in cultural heritage.

The image of slave owning Cherokees – even an elite minority - can be difficult to reconcile with the legacy of the Trail of Tears (crucially, it does not invalidate that injustice). In an interview with Smithsonian Magazine, museum curator Paul Chaat Smith (Comanche descent) does not mince words, saying “The Cherokee owned slaves for the same reasons their white neighbors did. They knew exactly what they were doing…They were willful and determined oppressors of blacks they owned, enthusiastic participants in a global economy driven by cotton, and believers in the idea that they were equal to whites and superior to blacks.”

Runaway notices from the antebellum period show that slaves both escaped to native communities and from native communities. Or at least, their masters speculated they were escaping to native communities. The National Parks Service hosts a few transcripts from the Arkansas Gazette that demonstrate this:

April 7, 1821: a runaway notice posted by W.M. Watson, stating that his slave Austin “will no doubt endeavor to make his escape to the Cherokees”

September 19, 1832: a runaway notice posted by James Wand of the Cherokee Nation

July 3, 1839: a runaway notice posted by John Williams of the Cherokee Nation

January 31, 1851: a runaway notice stating that the runaway will likely seek refuge near his wife in another county “or the Indian country”

March 7, 1851: a runaway notice posted by E.J. Smith, speculating that his slave Bob “if not stolen, he in all probability has gone to some of the neighboring Indian nations”.

June 25, 1859: a runaway notice posted by Thomas S. James, supposing that his slave Dick “in company with some other runways, is aiming for the Indian Nation”

Such postings continue through the Civil War. In a notice posted in the Washington Telegraph on July 20th, 1864, we see that four slaves escaped from their master in the Choctaw Nation in Oklahoma. See Fugitives from Injustice: Freedom-Seeking Slaves in Arkansas (particularly Chapter Two) by S. Charles Bolton for a more in-depth look at the relationship between the resettling Five Civilized Nations, white settlers, and escaping slaves.

It is not a clean answer, but to reiterate, there is evidence for both slaves running away from and to native communities. Another important point somewhat tangent to this is that slaves also ran away to their own communities, called maroon settlements. The most notable North American maroon settlement would be in the Great Dismal Swamp, covering parts of southeast Virginia and northeast North Carolina (Aptheker). In the early 1600s, Native Americans fleeing colonial frontier settlements went here, and were shortly joined by fugitive slaves and potentially some whites escaping indentured servitude. From roughly 1680 to the Civil War though, these swamp communities were dominated by escaped African and African-American slaves. They lived in freedom, though it was an uneasy existence. Even if not directly escaping to Native Americans then, escaped slaves in maroon settlements can be seen as carrying on resistant, permanent communities established by and with Native Americans.

Sources:

Aptheker, Herbert. "Maroons Within the Present Limits of the United States." The Journal of Negro History 24, no. 2 (1939): 167-84. doi:10.2307/2714447.

Bolton, Charles S. "Fugitives from Injustice: Freedom-Seeking Slaves in Arkansas, 1800-1860." National Underground Railroad Network to Freedom, (2006). https://www.nps.gov/subjects/ugrr/discover_history/upload/Fugitives-from-Injustice-Freedom-Seeking-Slaves-in-Arkansas.pdf

Doran, Michael F. "Negro Slaves of the Five Civilized Tribes." Annals of the Association of American Geographers 68, no. 3 (1978): 335-50. http://www.jstor.org/stable/2561972.