This method is never called by the POI code, and none of the built-in implementations have meaningful implementation of the method. PackagePropertiesPart#flush() was called in one location, but as the implementation is empty, the call is unnecessary. There's no bug here, rather, there's just code that is essentially dead.
PR available https://github.com/apache/poi/pull/202
I don't think we want to implement this - Marius closed the PR - Marius, please feel free to reopen if you feel strongly about this.