Reportedly get The Kinks out of distress (8)
I believe the answer is:
straiten
'distress' is the definition.
(I know that distress can be written as straiten)
'reportedly get the kinks out' is the wordplay.
'reportedly' shows a homophone (sound like).
'get the kinks out' becomes 'straighten' (straighten can mean to remove kinks from something).
'straighten' sounds like 'STRAITEN'.
'of' is the link.
(Other definitions for straiten that I've seen before include "distress" , "Train set (anag.)" , "Restrict" , "Limit" .)