I live about 12 miles from Coeburn, and we have a 42'11" fifth wheel pulled by a dually pickup. We have no problem making this trip and make it at least twice a year. We don't go all the way to McClure, but big coal trucks travel those roads each and every day, so other than passing them on a 2 lane road, you couldn't have any problem. (That is only from Coeburn to McClure or Clintwood.
So if I were coming from Hickory, I would travel I-77 to Wytheville, VA. I-81 south to Abingdon, VA. Take exit 14 and travel Alt Rt 58E to Coeburn, VA. I would take Rt 72 out of Coeburn towards McClure.
If I were coming from Asheville, Take I-26W to the TN/VA line where it turns into Rt 23. (Google"The Crooked Road" if you are interested in Bluegrass Music). Rt 23 runs right by Hiltons, VA (Carter Family Fold), but continues on to the Ky border (4 lane limited access highway) In Norton, you will leave Rt 23 and merge onto Alt Rt 58W to Coeburn.
Where are you planning to camp? PM me for some suggestions if you don't have a plan.