I'd say Union Jack as that makes it more distinct, but I know it is the Union Flag. To me, Union Flag does not sound particularly British. I will give you some context so you can help me decide how it should read in the story. —The sweet alluring smells from the pub were more what those fellas were expecting; definitely an English thing, although it soon became somewhat more American. The Stars and Stripes stood next to the Union Flag, or Jack as they liked to call it. The Americans seemed to have a way of just taking ownership of things and the locals being typical Brits made no fuss. Little details that made their allies feel at home were just fine and if anything, life was infused into the now swelling community. In time The Rusty Hook became as much an American thing.—
It's commonly referred to as the Union Jack. I wouldn't let correctness over something this nitpicky worry you if you prefer 'Union Jack' in context.
As you probably know, the Union Jack is the Union flag when it's flown from a ship. But yes, to most people, Union Jack is more recognisable.
If this still matters to you, I'd say go with Union Jack too. First thing I thought about at Union Flag was that flag on the roof of the General Lee. I don't even know for sure if that's the or a union flag right now, but that's where my mind went. Edit: Apparently it's the Rebel Flag I'm thinking of. And I think that means I need to apologize to someone.
Union Jack. When I hear Union Flag, I always wonder which union for a moment. And the idea that it should only be called the Union Jack when flown from the bows of a warship appears to be an urban myth: https://www.flaginstitute.org/wp/british-flags-2/the-union-jack-or-the-union-flag/. Of course, some people will read Union Jack and be annoyed that you called it that. But those people are both pedantic and wrong.
I disagree. The "rebel flag" is a historical artifact of the American south and unfortunately has been co-opted as a symbol by racist morons. The flag itself is not inherently good or bad, it is how it is being used and what it used to represent that have combined to give it a bad reputation. I really think it needs to be reclaimed and used properly, in its historical context. Bah, my opinion only, and I'm a Canadian so what do I know.....
I live in Scotland, and I've only heard it referred to as "The Union Jack." It makes sense, because 'The Union Flag' is awfully vague, really. It would only make sense if the readers know exactly what 'union' is being referred to. Scotland has two flags ...the blue cross of St Andrew, which is called The Saltire, which anybody can fly. And the coat of arms on the yellow background which is referred to as The Lion Rampant. Although now officially restricted to use by representatives of the Monarch and at royal residences, the Lion Rampant continues to be one of Scotland's most recognisable symbols. These are kind of like the USA's flag which is sometimes referred to as "Old Glory" or, more commonly, "The Stars and Stripes." Kind of a nickname, but it has become universally recognised as the name of the country's flag.