Random firefighting tidbit: after structure fires, if you were in the heat for a good while, it was a dick move to slap your buddy on the shoulder/back like "good job" because if you did, the insulation in the bunker coat would compress, and they'd get a raised welt on their skin with a mild steam burn and a hilarious hand print.
Firefighting equipment is fascinating that it works at all
With a steady supply of cold'ish water I would guess it would do a decent job of keeping you chilled, and not on fire. Maybe? This is similar in function to systems they deploy on some firetrucks that could be in danger of getting trapped in a burnover. Of course, those keep a truck exterior cool, not an early 20th century raincoat.
Either way, it looks wildly impractical, and the user must have a hard time seeing much.
My dad was a firefighter and showed me the various nozzles they used on the firehose. One of them worked kind of like this, except it sprayed out of the hose (obviously), and created a shield-like spray in front. It was used mostly for cooling down hot air and combustible gases. It also carried the benefit of soaking the corridors you were walking through. If you're caught in a blaze, nothing will help you, but for anything else, this would be pretty useful.
In an intense fire this just made thing worse. Especially for the person wearing it. Plus supplying water to this was not ideal either. Especially as the water used here is water that couldn't be pumped into the main hose.
This would make it so much worse. Water would just increase the heat transfer to the wearer.
Good home example, if you wet an oven mit and try picking up a hot pan with it, it will burn your fucking hand. If it was dry, it wouldn't transfer the heat as fast.
Why post with so little detail for the date? It's vaguely informative, sure. But it is the 1900's, surely we haven't lost this knowledge and need to date it like ancient egytian archeology.