There is a long and complex history of the interaction between Christians and the state which makes me hesitant to answer too definitely whether or not such things are good, since to do so it is necessary to look at them abstractly, which to me makes any answers less illuminating than they could be.
I remember once asking our priest why we pray for the king (president) of the land, and refer to him as God's servant in prayers said during the liturgy if in Egypt this hasn't really ever been the case (NB: Egypt was a Christian country by the confession of the majority of its people for several centuries, not by the conversion of its king, unlike in other countries like Ethiopia or Armenia, which had Orthodox Christian monarchies). To the best of my recollection, he said that this prayer was placed where it is in the liturgy among various petitions asking God to safeguard various aspects of life in Egypt because it was often not safe. So we also pray that God bless the land and make it fertile, because if it isn't, people will die. We pray that God keep the church or the monastery safe (as in the literal building that we are in) because it was common in the old days for those places to be attacked by bands of robbers or other hostile forces (St. Moses the Ethiopian, one of our most famous saints, had once been one such a robber, and later was killed by them together with other monks of the monastery). In light of this, praying for the leader is our way of both recognizing that God has the authority in all situations (so if we have a bad leader, as we usually did then and do now, we will still pray for him, rather than cowering), and that, if given the choice, we would rather that he be God's servant than not!
I think I'd have to answer these questions only in that sort of light. If it is patriotism with a view towards wanting to live in a peaceful country, where safety and dignity are respected, and the people are not exploited by their government, then there's nothing in that which a Christian should feel hostile towards. Whether or not that's actually what's going on in any given country is a different story, but as far as patriotism is concerned, I think a certain type of it can be healthy, if it inspires people to make their community's better, rather than just waving a flag to show their patriotism or whatever. I think it's a million times more patriotic to feed the hungry and comfort people who are suffering than to recite some pledge that basically amounts to declaring allegiance to abstract concepts like 'liberty' or whatever. What's liberty to your neighbor who is starving, or the family down the block who are freezing because they can't pay their heat bill?
Nationalism...ehhh...I guess you can find a lot of it in Christian churches, in the sense that the particular form of Christianity that is embraced in the oldest still-existing Christian communities (e.g., the Greeks, the Copts, the Syriacs/Assyrians/Aramaeans, etc.) tends to have something of a 'national' character to it by virtue of being a part of how particular ethnic groups tend to identify themselves. But that's because it's so old, not because those people by definition think that they are better than anyone else. I mean, for sure there are probably some who do, but at least from my experience with the Copts, it's more confusion or curiosity about the rest of the world. Like the bishop of Asyut famously said to the Presbyterians who came to Egypt in the 1860s looking to 'convert the Copts to Christianity' (hahaha), "Our people have been living with Christ for almost two thousand years; how long have your people been living with Him?" When you are indisputably the first people of your location, and you know that, you don't really need anyone else to tell you your business.
But that's miles away from the standard American (and Arab, and European, and every other colonizer's) narrative that since they bring such great things to the world they ought to be thought of in exceptional terms. That's ridiculous (just ask the rest of the world!). Places are what the people in them make them, not because of some essential 'Americanness' or whatever that makes them so great. So I don't think that's a good attitude to continue in children, or adults for that matter.
