The Cunningham-Flenniken Cemetery dates from around the 1790s. I found a local blog post from 2007 that says the cemetery dates back to 1799. I also found an academic paper online entitled "Investigations at the Cunningham-Flenniken Cemetery, Knoxville, Tennessee." Here is what it says:
Cunningham-Flenniken Cemetery
"The Cunningham-Flenniken Cemetery (40KN82), located on the crest of a high ridge (elevation 920 MSL) 30 miles ( 48.3 km) north of the south bank of the Tennessee River and east of the South Knoxville Boulevard Bridge, is one of the oldest burial grounds in Knox County, Tennessee. A concentration of burials, organized in clusters by family, are on top of the hill, with dispersed graves on the east and south slopes. A separate group of burials is located on the north slope of the cemetery ridge. Many 19th century cemeteries, particularly in the Southeast, are located on high ground due to the need for preserving agricultural land (Jeane 1978:896).
The cemetery was originally established as a family burying ground in the late 18th century by Robert Cunningham, an early Anglo-American settler of south Knoxville. In subsequent years other families such as the Flennikens, Simpsons, Kirkhams, Maxwells, Kings, Youngs and others were allowed to bury their dead in the cemetery, most likely as a result of marriage or community ties to the Cunninghams. The connection between these families remains uncertain, although further census and city directory research may yield definitive social ties."
I think that the part about the cemetery being 30 miles north of the south bank of the Tennessee River must be a typographical error.
Location: 2437 Anita Drive, Knoxville
Northeast corner of Anita Drive and James White Parkway/Cottrell Street, on the south side of the Tennessee River.
Info Source- Robert McGinnis' cemetery database.