The short answer is to do as much of this on the main BA.com website rather than the App since it seems to handle >24 hrs OLCI better than the App.
But you can get to the main BA.com on the App via the Manage My Booking link the App's Manage My Flight screen, bottom of the screen. This doesn't produce a conventional App boarding pass but it can do (e.g.) a PDF boarding pass and most places are OK to use PDF on a mobile device or tablet.