What is the difference in meaning and usage between the nouns “stream”, “flow” (“pour” is excluded from this list based on comments) and probably other words with similar meaning? What is more appropriate when talking about news or other entities of content continuously appearing on a website, other discrete object constantly appearing on one side, moving to other and disappearing there?
When I hear or read the word, stream, first of all I think of a fast flowing, rather narrow, fresh water river. So these word associations fit rather nicely when we talk about something that is constantly moving, and always renewing itself (fresh).
If I am sick in hospital I can say: I had a constant stream of visitors.
An online newspaper website will provide: a stream of news articles.
A 24 hours news programme will boast: Live stream coverage from ABC News
Flow on the other hand, usually describes how liquid runs continuously in one direction, its meaning is quite similar to (a) stream but it lacks the idea of being constantly updated; fresh and new. It is however, in my opinion, more versatile.
Flow is normally collocated with hair, liquids, rivers, alcohol, words (written and spoken), ideas, traffic and information:
There are many other collocations with flow which you will find in any good dictionary. Some you may be able to substitute with the noun or adjective "stream" for example, information, others much less so.
I would say that it is very uncommon to use the word flow in the context of:
Stream in this context commonly refers to live video.
The word you are looking for as mentioned in the comments is feed — this is the commonly used noun for content continuously appearing on a website.
You're asking about a metaphor.
Before you think about the words, get the metaphor fixed in your mind.
Write up the metaphor frame -- a long description of the metaphor as you see it, but be literal. Use all the fluid verbs you can think of, but use a term for a fluid in the description, instead of news.
Then substitute news for the fluid and see which ones are cliches, which ones are just too weird, and which ones work. There'll be some of each for every metaphor frame.
For more about frames, see Framenet.