你也可以说 （你）看，那有一只鸟正在飞（假设你和你同学在聊天，你突然看到了一只鸟，你可以这么说，这样的说法在口语中更常用） 其他的例子： （你）看，那里有个奶茶店 （你）看，那有辆车

If I were to mean look at the bird that’s flying over there, I would have phrased it something like 看那儿有只鸟在飞. It’s not a literal translation. Since we don’t have subordinate clauses in Mandarin, translating them from another language can be quite flexible. The 2 sentences you write are correct, but I doubt it’s what people say in real life.