Missing the point
You may not have noticed, but the concept of an airline having a 'nationality' from a commercial/legal point of view is diminishing. Within Europe, there is no such thing as a 'German' carrier, or a 'British' carrier or a 'Maltese' carrier - just an EU carrier which is defined as one majority-owned by EU nationals. So for example a German-based airline can operate UK domestics or an Irish-based airline can set up hubs here there and everywhere.
The EU-US agreement is an extension of this process. Any EU airline or any US airline can fly any EU-US route. Seems to me perfectly appropriate to carry those two flags, if you're going to show any flags at all.
Of all the main European carriers, I suspect BA is the one whose ownership structure comes closest to falling short of the limit of 'majority owned by EU nationals',
The SSK
(a European of UK descent)