I assume you're talking about Nixie's Resident TOS, because it sounds like you're talking about using email alerts to compile your own alerts with another data source of flood watches/warnings.
If so, you're not accessing the data by bot or scraper or spider, and I'd say you're not be in violation of that part of the TOS you quote.
But the other part of the Resident TOS (the Grant of License section, right after the above part on the Nixie site http://www.nixle.com/terms-of-service/) reads (my emphasis):
As a user of this Web Site (an “Individual User”), you are granted a
personal, nonexclusive, nontransferable, non-assignable, revocable,
limited license to access and use the Web Site, Services and Content
for Authorized Use only and not for commercial purposes. “Authorized
Use” means your use for non-profit or informational purposes, but
DOES NOT include (a) using the Services, Content, or parts of the Content, for for-profit gain for any party, individual or entity, or
(b) the posting, publication, transmission, or dissemination of the
Content, or parts of the Content, in digital or electronic form by
means of the World Wide Web, electronic mail, any online services, or
any other medium now existing or hereafter developed. Otherwise, you
may not duplicate, transmit, redistribute or publish the Content, or
parts of the Content.
What you want to do is redistribute their content, which is against the TOS.
You're not simply analyzing the data you get in their emails; you are receiving it, analyzing it, compiling it and redistributing it. Yes, your content is a new product by virtue of your compiling and processing that email data and your own data. But you're still redistributing their data.
True, the TOS does not specifically say you can't combine their data with your own and then distribute it. But, I'd say their attorney could easily make that argument, when Nixie found you redistributing their content, they could change their TOS and kick you off their service, at very least; at most, maybe take you to court.
Maybe the easiest thing to do is simply ask Nixie if you can get their data by email, compile it and redistribute it in the way you want for your app. They may go for it, they may not. (Their Agency TOS also prohibits redistribution of content). But you will know for sure if you are a legal user of their data under their TOS.
As a side note, there's a chance Nixie would want to provide their data via an API and in a consistent and (mostly) uninterruptible stream for the reliability of your own app. If you gather their data by email, and Nixie's email goes down, or gets flagged as spam by your email client system that receives the email, your app and data collection is disrupted.