Fiery, being of S American lineage (12)
I believe the answer is:
incandescent
'fiery' is the definition.
(thesaurus)
'american lineage' is the wordplay.
'american' becomes 'incan' (I have seen 'Old American' mean 'incan' so perhaps 'american' could also mean 'incan').
'lineage' becomes 'descent' (synonyms).
'incan'+'descent'='INCANDESCENT'
'being of s' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for incandescent that I've seen before include "Glowing with heat" , "Furious" , "livid" , "Mad" , "Brilliant" .)