By default, every time Chunky crashes it sends info about the crash to the crash-reporting service Crashlytics.
I get to see where in the code the crash happened, and some basic info about the device it crashed on (make and model, free memory, that kind of thing). I don't get any personal info about you, or your library.
Crash-reports are really vital to me learning about problems that would otherwise be impossible to diagnose, but you can disable them by going to the Settings menu, hitting 'Advanced', and turning off 'Send crash-reports'.
3rd party storage providers
When you add a 3rd-party storage service to Chunky (eg. Dropbox or Google Drive), Chunky will communicate directly with that service to let you browse your files and import comics to the app. It will not share any data from this service with anyone.
Chunky does not collect any oher data on how you use the app, beyond the standard anonymous iOS analytics. You can disable these analytics using the 'Share with App Developers' setting in the Privacy section of the Settings app.