I saw this on YouTube – The 40 Minute War – YouTube Video War Documentaries: https://www.youtube.com/watch?v=7BTS8NH-E0I (about 1:06 minutes long), but I knew about this war long before the Internet was something many people could use. According to this Wikipedia article – https://en.wikipedia.org/wiki/Anglo-Zanzibar_War, the Anglo-Zanzibar War lasted around 38 – 45 minutes.
I learned about this war the old fashioned way. Looking at the back of my encyclopedia set. Back then, there were sections at the back of each volume on things that didn’t qualify to be main articles in the front of the encyclopedia. That’s how I learned about Emperor Norton I, the Anglo-Zanzibar War, etc. I would thumb through these mini-articles. Or, I would dig through the card catalogs, including the magazine catalogs, at my school or public libraries.
Here are some other links:
Atlas Obscura: https://www.atlasobscura.com/articles/worlds-shortest-war
Encyclopædia Britannica: https://www.britannica.com/event/Anglo-Zanzibar-War
South Africa History Online: https://www.sahistory.org.za/article/anglo-zanzibar-war-1896