So unfortunately, I do not have a ton of information on this, but was able to track down a plausible answer. Big caveat is that I am not a professional and can only point you to a better direction. With that said:

Adrienne Mayor, a Stanford historian on ancient science, mentions in one of her books about Mamluks using naphta attached to their bodies as an intimidation tactic. Their clothing would be made of fire-retardant material, such as asbestos. That looks like what the middle fellow is doing here. I'm afraid I don't have the book on hand, so cannot provide more details.

Here's a tweet from Mayor referencing that act with a contemporary recreation and a treatise depicting it.

This is the book if you are curious for more: Greek Fire, Poison Arrows & Scorpion Bombs: Biological and Chemical Warfare in the Ancient World