To add yet another answer to a long list of good ones, this is what I would advise:
- Do not use "short", as in "short news".
A news article can be short, and other kinds of news reports can be short, but it makes no sense to talk about the length of news itself. (For one thing, news is used as a 'mass noun', so there is no such thing as a news. More importantly, the word refers to the actual events, not specific reports on them (unless you add "report", or "article", etc.)).
That term means that the news is being delivered with little delay. It does not refer to how much time it will take to read, listen to, or watch the news report. The term "news flash" also carries a connotation of importance (because very important reports are the ones that are more urgent to deliver with little delay (perhaps interrupting regular programs on TV, for example)).
- Using "quick news" would be OK.
This is similar to "short news" but much better. It is still a bit confusing to use an adjective referring to how much time is required to take in the news reports (reading etc.) and not referring to the news items themselves, but it is much more intuitive than with "short" (probably because a news item can't have a speed, but it almost makes sense for it to have a length, so it is clearer that "quick" must refer to something else).
- Using "news ticker", as suggested by others here, would also be OK.
Some people might be more attached to the word "ticker" meaning continuous updates on a single specific measurement, but as long as you have it with the word "news", it is fairly clear what you mean, since it is called a "news ticker" on so many video news programs. I get the impression that your feed scrolls as new reports come in too, and that is a hallmark of a ticker.
- Use "news digest" or "news snippets" if you specifically want something that refers to the reports being short.
A "digest" is a compilation, and can also convey abridgement (shortening, summaries). It really does sound like exactly what you what. There is a chance that people less familiar with English would find "snippets" easier. This word sends a bit of a different message, though, since it refers to a part of something instead of a summary of something.
- Use "news feed" or "news stream" if you just want to convey that it is live and stays up to date.
This does not really suggest that the news reports are short, but if the title is only seen when you can already see some reports, then you may not need to point out that they are short. Of course, you may still want to go with "digest" or "snippets" to keep it clear in the mind of the user that you do have that longer-form news section you mentioned.