This app does connect to the internet to fetch RSS feeds. When you add a feed, the privacy statement of the feed publisher applies.
No data is uploaded by the app to any servers (except the requests that have to be made to download the feeds).
Settings on the device will be stored on the device and might get backed up to iCloud if this is configured in the users iCloud preferences.
This statement does not cover functionality that is provided by Apple (eg. the App Store analytics).