Could John R. Floyd be the son of Wright Floyd, son of Frederick Hardee Floyd ? Wright Floyd was born in 1801/1802 in Horry Dist, SC. He died after 1870 in Horry Co, SC.
From 1840 census (Family Search citation below) in the household of "Right Floyd":
1 Male 30 - 40 ("Wright" Floyd)
1 Male 15-20 (Unknown son of Wright Floyd)
1 Male 10-14 (James Floyd)
1 Male 5-10 (Unknown son of Wright Floyd)
1 Female 30-40 (wife of Wright Floyd - probably Demaris Adams)
1 Female under 5. (Sarah Floyd)
"United States Census, 1840," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:XHYL-4F4 : 19 August 2017), Right Floyd, Horry, South Carolina, United States; citing p. 325, NARA microfilm publication M704, (Washington D.C.: National Archives and Records Administration, n.d.), roll 512; FHL microfilm 22,509.
Is the oldest "Unknown son" John R. Floyd? Additionally John R. Floyd named one of his sons William Wright Floyd and John R. is buried in with the descendants of Frederick Floyd in Riverside Cemetery, it seems to be a plausible explanation. Y DNA testing may help with this through the Floyd DNA project. One son is noted by Marty Grant as confirmed somehow. There could be at least two more if the census is any guide.