The following are all the fully flat options available:
US C and TG C (The CDG has a leased aircraft with these
fully flat seats): CLT-CDG-BKK (4 hours connection time)
SQ C: CLT-EWR-SIN-BKK
NH C and TG C (TG has the same leased aircraft on the NRT-BKK route): CLT-JFK/ORD-NRT-BKK
OZ C: CLT-LAX/SFO-ICN-BKK (ICN-BKK is angled flat)
LX C: CLT-JFK/MIA/ORD-ZRH-BKK
AC C + TG/NH/CA C: CLT-YYZ-(YVR)-PEK/PVG/NRT-BKK
+ Some routes with UA and CO.