Trumpy raises a good point that needs some differentiation. Leather may not burn in the conventional sense like synthetic fabrics, but it will probably weaken when exposed to significant heat from, say, an arc blast.
It may seem obvious, but a “tool belt” for the sole purpose of strapping hand tools at your waist would not be evaluated the same as a safety restraint holding one to a pole or ladder. Clearly though, there are “combination” belts that will do both.
Hugh Hoagland—a safety consultant in the US—has a site with some data on arc-blast performance of occupational gear at www.arcwear.com
In his online movies, it is not hard to imagine that leather under stress would likely “flunk” miserably.