Alexis Madrigal has a widely-cited piece suggesting that we may have seen "peak rivers" in 2013. (He calls them streams, but streams and rivers are the same thing.)
I think we're just getting started. We've created just a few big flows, commercialized them, and they're somewhat clogged, but that doesn't mean that river transport is done for. We may find the leading flows, Facebook and Twitter, to be too sensational, commercial, or superficial. Perhaps not enough to sink our minds into, but that doesn't mean some information isn't best presented as a flow.
Consider news about the NBA. Every night there are scores, reports of injuries, rumors. The next morning, gossip, analysis, stats, trivia, more rumors. There's a very predictable beat to sports news. Lends itself to a river. Yet, I just got my river going last week! I've barely begun to understand the new experience.
I think we'll discover many more uses for reverse-chronologic flows in 2014, 2015 and so on. It's a very basic format. The teletype was a river. Stock tickers are rivers. That doesn't mean there aren't databases, and books, think pieces, taxonomies. A river is just one structure, but it's a good one, and we don't throw good structures out.
PS: Interesting his piece appears on The Atlantic, another body of water.
PPS: Think of a river as a format, like "romantic comedy" or "spy thriller." They keep making them, generation after generation. They change with the times and technology, but the formats are in our brains, not in any one medium.