Turn on War Mode and have at it
If you’re into world PVP, you’ll probably have a great time with WoW Dragonflight. In fact, even if you aren’t, I recommend turning it on and giving it a go! You’ll get some random and easy rewards as a result: including War Supply chests. Here’s how to find them.
War Supply chests/crates drop from the sky with War Mode (PVP) on
In each zone, War Supply crates have a chance to spawn and appear on the map. An NPC will yell a quote about “survival of the fittest,” letting you know that a supply drop is coming: denoted by the exact icon in the gallery above (a circle with wings coming out of it). Head over to the supply crate to claim it.
Alternatively, you can create a farming group (which can also protect you from the other faction), and stake out each zone. Once you hear the call, hearth to Valdrakken, then fly out to the marked area.
After you claim them, loot them with the random or premade group
To claim a chest, you just need to channel it for a few seconds without being interrupted by the other faction. Once someone claims it, it will be available to loot by everyone in that faction for a short time. Keep this in mind when people message things like “war supply crates available at [X/Y] coords.”
That’s it! Feel free to farm them to your heart’s content, just remember that it is a PVP activity (though you can benefit from that even further with PVP on).