The "NOW Corpus" (described at https://corpus.byu.edu/now/) apparently consists of articles copied from various online publications, primarily online versions of magazines and newspapers. These originate in the US, the UK, and India, and perhaps other countries. A number of the listed publications are well-known, commercial publications and are surely protected by copyright.
It is not clear to me under what license, if any, access is provided.
The publishers say that they obtain the articles via Google News.
The publishers of the corpus say that about 10,000 articles are added to the corpus every day. The publishers sell access to the corpus. Limited access is also provided free of charge.
The publication seems to be aimed at linguistic research, and research into the usage of words and phrases in published English. However, the publishers don't appear to attempt to limit the purposes for which someone may access the corpus. The publishers assume that all use is NON-commercial.
In their FAQ item on copyright, the publishers say:
Our corpora contain hundreds of millions of words of copyrighted material. The only way that their use is legal (under US Fair Use Law) is because of the limited "Keyword in Context" (KWIC) displays. It's kind of like the "snippet defense" used by Google. They retrieve and index billions of words of copyright material, but they only allow end users to access "snippets" of this data from their servers. Click here for an extended discussion of US Fair Use Law and how it applies to our COCA texts.
In their extended discussion they say (in part):
Under no circumstances whatsoever do end users have access to entire texts (e.g. newspaper, magazine, or journal articles, or short stories). All access is via the web interface, and the vast majority of what users see are simply frequency charts showing the frequency of words or phrases in different parts of the corpus. Access to small portions of the original text is more of an "afterthought", rather than the central feature of the interface.
To avoid infringing on copyright, usage of text from this corpus would apparently need to comply with the fair use conditions, as the text does not seem to be available under any sort of free or permissive license. The publishers suggest how this can be justified in the FAQ and discussion linked above. Whether a court would agree is another question.
How an application might use this text would greatly influence whether such use would be justified under fair use (in the US) or fair dealing or some similar principle (elsewhere). This will involve very specific facts about the app, and a lawyer knowledgeable about copyright law in the jurisdiction of the app publisher should be consulted.