Flat broke meant pinching to some degree (9)
I believe the answer is:
apartment
'flat' is the definition.
('apartment' can be a synonym of 'flat')
'broke meant pinching to some degree' is the wordplay.
'broke' is an anagram indicator.
'pinching' indicates putting letters inside (taking inside).
'to some degree' becomes 'part'.
'meant' is an anagram of 'ament'.
'ament' enclosing 'part' is 'APARTMENT'.
(Other definitions for apartment that I've seen before include "Flat (chiefly US)" , "property" , "Penthouse" , "place to live" , "pad" .)