The following document will help you access the read-only Gmail inbox feed.
About Atom
Atom is a system which makes it easy for you to receive, in one place, regular updates from news websites, blogs, and/or Gmail. You can use Atom with an aggregator (also known as a newsreader, feed reader, or RSS/Atom reader) to receive new message alerts.
Using the Inbox Feed
The Gmail Inbox Feed will output your Inbox as an XML document. You can use
an RSS aggregator to view this, or you can consume the feed with your own app.
OAuth 2.0 is the preferred authentication method,
using the scope https://mail.google.com/mail/feed/atom and fetching the feed
with the request GET https://mail.google.com/mail/feed/atom.