Hello John,
The 69th Irish Brigade Regimental flag presented to the Irish Government is / was a New York State Military flag, not a U. S. Government flag. No data on it, but I would imagine that President Kennedy had permission from the New York Governor to gift the flag as a way to honor all of the Irish immigrants that fought on both sides of the war. Many of whom could not get out of the Federal Military draft for the lack of the $300 get out of the draft fee. The riots in New York City was a protest of that draft and there was also a secession movement in New York City, to join the Confederate side of the war, States Rights. President Lincoln had to send Federal Troops, fresh from the Battle of Gettysburg to put down the draft riots and secession movement.
The Irish fought hard and honorably on both sides of the war to maintain their idea of freedom from an oppressive Crown, as did many other ex-British subjects, to be freemen in these united States. It could have been these united Confederate State, but.
If, perhaps, the entitled Crown did a better job of preserving their honored flags, I could half agree with you. But since they are just beloved figure heads, maybe the British Government could do a better job.
As a side note, Several Irish Confederate flags where sent to Ireland after the war. They to, are missing from public view.
Happy Trails!
Tom Martin