Part of influenza, chest pain (4)
I believe the answer is:
ache
'pain' is the definition.
(ache is a kind of pain)
'part of influenza chest' is the wordplay.
'part of' indicates the answer is hidden within the clue.
'ACHE' can be found hidden inside 'influenza chest'.
(Other definitions for ache that I've seen before include "Suffer dull pain" , "Each (anag.)" , "suffering" , "Longing" , "yearning" .)