While LibreOffice’s Android port has as good support for ODF as the desktop version, flat ODF was lagging behind. There were two reasons for this:
flat-ODF-related services were simply missing from the .apk, for historical reasons: when the .apk limit was 50MB, it sounded like a good idea to leave these out if it allowed packaging e.g. editing-related services.
flat ODS was blacklisted explicitly, from the times when Calc tiled rendering was missing, and when .ods was included again the document browser, .fods was forgotten.
With these two fixes my favorite test documents (of which the ODF version worked already previously) in flat ODF version also load properly in all Writer, Calc and Impress — as can be seen on the above montage of screenshots.