One of the best iOS RSS reader apps for offline browsing is 'Reeder 5'. It is a powerful and user-friendly app that allows you to read and manage your RSS feeds even when you are not connected to the internet. Reeder 5 supports various cloud services for syncing your feeds and reading progress, and it also offers a clean and customizable reading experience. With its dark mode, multiple themes, and support for a wide range of RSS feeds, Reeder 5 is an excellent choice for anyone looking for an offline RSS reader app on iOS.