I actually did some work like this, back when I wrote my master thesis, although on a quite smaller scale.
I wrote about Danishminded POWs in Russia during World War 1, a group of approximately 300 people and obviously some of them died in captivity, but it wasn't possible for me to reach a figure closer than between 10 and 50.
Why?
Main reason is that in history, unlike in archeology, dead men usually tell no tales. They don't leave any letters or sources, they just stop at some point. And obviously not everyone are regular writers at all.
I also restricted myself to using only Danish archives, as I could piece a quite good puzzle together using the archives from a POW veteran organisation and a charitable organisation devoted to helping the POWs. Both had a list over prisoners and by crosschecking and adding a bit, I could figure out a pretty accurate estimate over the total number of POWs. The lists of both organisations where around 220-230 and in total it was around 250 positively identified.
Both organisations noted down the number of prisoners who they positively knew died in captivity, but it was a quite low number, around ten. from reading general literature on POWs, I could figure out that if the deathrate of Danish POWs were equal to German or Austrian, the number should have been higher, around 50. This doesn't necessarily need to be the case, as Danish POWs had the chance to go to special treatment camps, but only around half ended up there. The rest went to regular camps, some of them real typhoid traps.
I could probably have reached a more accurate figure, if I had used German and Russian archives as well, but since I wasn't writing a book, I didn't think it would be worth the effort. Archival work can be pretty exhausting, even if it's "just" in your own language. Also, German army archives burned after being bombed in WW2, so the most likely place for me to look in Germany doesn't exist anymore.
With regards to the Spanish Flu, I imagine that one of the main reasons for the inaccurate numbers, is the problem with compiling all the data. Before the internet, it was actually quite hard to get info like this from other countries. A good university library was a necessity. Also, I'm pretty sure that most European countries would have relatively reliable figures or it should be possible to reach them, but since it was a global pandemic, it must be hard to estimate for the rest of the world.
If anyone is looking for a subject for a paper, thesis or maybe even a ph.d. tho, imho this is definitely not the worst place to look.