Clue: Flaw in insignia, which should not be part of a straitjacket (8)
Answer: ARMHOLES
Explanation: Definition: which should not be part of a straitjacket
An envelope ('in') of HOLE ('flaw') in ARMS ('insignia'). I would take ARMHOLES to be the shoulder openings, which a straitjacket would have; it seems Brummie is thinking of the cuffs.