The flag is the same flag as the Council of Europe, which BTW we are still a member of. 
The "anthem" predates the EU by a long way
and is also the anthem for the Council of Europe. It was adopted as the words, written in 1785, (and put to music by Beethoven in 1824) were deemed to be appropriate, first by the Council of Europe (in 1972) and then by the EU heads of state (which, BTW, included the UK) in 1985.
Or are you going to complain about the "anthem" for the rugby World Cup and other such "anthems" 
The EU "army" is a Brexiter myth put the about by mischief makers. There is a very small peace keeping force that the various sovereign countries contribute to, but because defence is still the sovereign countries' responsibility and because the sovereign members have a veto over the creation of an army, it was never going to happen
.....although maybe with an aggressive island just off its north west coast, who can no longer add its veto to the process, it might change its view about the requirement
(seriously though: it's never going to happen, as all the sovereign countries have different attitudes as to what/how an army does/functions/trains, and anyway, as most EU members plus a few neighbouring countries are members of NATO, they are under a treaty obligation to treat an attack on one as an attack on all).
And as borntobequiet points out (reiterating what I'd posted earlier), if anyone wants to export to the EU, they have to abide by the EU rules. Only now we don't have a say in them. 
BTW: the EFTA countries might not on paper have a say, as they're not members of the EU but are in the Single Market, so need to abide by them, but because of that, they spend a lot on maintaining a significant lobbying group with the EU.
So many uninformed and fallacious myths. It's almost fun to repudiate them again and again 