It's related to the fact that most "traditional" county flags were based on the county coat of arms. You are not allowed to display someone else's coat of arms as it is the heraldic equivalent of passing off. Don't know what the penalty is, you'd upset the College of Arms or get eaten by Red Dragon Pursuivant or something. (This may be a made up name, I can't be bothered to search for actual herald's names.)
There was a famous case in the Fifties where Birmingham City Council sued a local cinema because they had the Birmingham coat of arms displayed on the fire-curtain.
So, I would guess there is case law and the learned opinion of a bunch of guys with funny Norman French job-titles. You'd probably be hung by the posset or something for infringement.
Since then people have been wary of displaying the council's flag.
Not sure there is any prohibition I can point to.
(Icon - coat of arms.)
Edit, sorry it was Manchester.
https://www.theheraldrysociety.com/articles/the-court-of-chivalry-some-reflections-on-the-manchester-case/
Biting the hand that feeds IT
