Hello Bill,
I think if you search on this site for terms like yosegaki or war flags or other such things, you can find a few threads with various kinds of flags. It seems that for every 4 flags we see, one of them might be authentic, and the other three will feel like Chinese fakes. When I say "authentic", I mean it feels like an authentic Japanese artifact, and not necessarily a war artifact. It isn't unusual for a flag to show up that just has signatures on it, and so there is no way of knowing if it was a wartime "good luck" flag, or just some random souvenir from a school or social club or something. So if your father brought this flag back from the occupation, I think it may have been a flag made and sold for much-needed cash - but no way to know unless there was a similar example with details of its provenance. I've never seen another flag with just drawings on it like this. It certainly is unusual. If there is any good news to come out of this, you can probably rest easy that it wasn't stolen off of some dead soldier, and instead was probably just a bit of memorabilia your father acquired.