Furnace or mill Ken and I rebuilt (8)
I believe the answer is:
limekiln
'furnace' is the definition.
(I know that limekiln is a type of kiln)
'mill ken and i rebuilt' is the wordplay.
'and' means one lot of letters go next to another.
'rebuilt' indicates an anagram.
'mill'+'ken'='millken'
'millken' after 'i' is 'imillken'.
'imillken' anagrammed gives 'LIMEKILN'.
'or' acts as a link.
(Other definitions for limekiln that I've seen before include "Oven in which a caustic substance is produced" , "Large oven for reducing calcium carbonate to 22 ac" , "Furnace (historic)" , "Producer of calcium oxide" , "Industrial heater" .)