I see a lot of posts about British people not being allowed to fly their country's flag at the risk of offense to the migrant populations there.

I do not see this reverse discrimination in Australia. The people I talk to in the U.K are unusually islamaphobic, and they talk about Muslims demanding that crosses be removed from Churches. However this accusation (designed to offend) makes little sense, because Islam accepts Jesus as a prophet, and if anyone was offended by an instrument of torture being placed on a church would be more to the sympathies to Jesus than to object to him, but regardless, Muslims have no prejudice against Jesus Christ.
As for this rule against flying the British flag, the cursory investigation I have done, I found this:
"Misleading. The quoted comment was made by a lawmaker, not the four English councils that were ​incorrectly attributed and whose flag-flying rules for public safety were misrepresented."

Now, skinheads in the U.K did used to plaster union jacks on their clothes, and soccer hooligans did like waving the Union Jack. I grew up in Wales, and tho there was plenty of violence there, I can't remember skin heads plastering Dragons over their clothes.

Skinheads and soccer hooligans were notorious for smashing in windows, kicking in doors and forming gangs for the purposes of violence. They like fighting. Generally when they were put in jail, it was not for waving a flag.

Just to add, if there really is this kind of reverse discrimination going on, then I can only believe that the motivation is to generate anger from the native population against migrants. That anger is aimed at the wrong place in that case. The source of this indignation is the Prime Minister of the United Kingdom who is allowing this to happen. And I would want him to be prosecuted for it, but I would not want his organs to be sold on the black market trade as was suggested to be done to British Muslims by one post on this site.