It's strange and doesn't really mean anything. I think it's a typographical or editing error.
I found your source here:
(It's a nice story and it looks like an interesting resource for easy English.) The author, Margo Fallis, does not appear to be a very famous author. Web searches mostly find her stories posted online at various websites, at no cost.
I don't think her story was professionally proofread, and an error slipped in. Perhaps she got confused or changed her mind about which direction the river was flowing--if it was a true river, it would always flow toward the sea; if it was an estuary, it might flow either way, depending on the tide. The following possibilities all make sense:
Together they headed for the river, which flowed out to the sea.
Together they headed for the river, which flowed into the sea.
Together they headed for the river, which flowed out into the sea.
Notice that the story is only about the river, so I'm not sure why she even mentioned the sea! The second and third possibilities would make sense if the story actually were saying something about the sea, for example, if they took their boat down the river and into the sea.
Now that I think about it, "flowed out into the sea" is curious--but it is completely natural English and a quick check shows that that phrase does appear frequently in books and articles. For example, a book about an excavation of a Viking site in Newfoundland says "We, too, went ashore where a river flowed out into the sea."