I know we're talking fantasy, but purple dye is pretty expensive. I don't know how cheap blue pigment is, but I imagine it's more expensive than using soot.
For dies? Depends upon the area for blue. Scotland? Blue was pretty easy - Woad. Sure, the prep is smelly, and the effects of application to skin are mildly psychadelic...
Middle East? far less so. But Purple can be had ... expensive but available. Everywhere else imports it from the eastern Med.
The easiest dies are yellows, oranges, and greens...
Soot isn't a dye - and for camouflage, that's both a benefit and a drawback - it means it comes off easier. It's also dry, so less glint. But if you sweat, you wind up with it migrating downward. Likewise, it's easier to remove by friction.
Likewise, dies on the skin are usually harder to remove - days or weeks - think henna, woad, or indigo - and usually rather rub resistant.
The most important element of camouflage - not actually known until the renaissance, and not implemented for nearly a century-
is breaking up the edges/lines... WW I was the rise of Camouflage, but the Spanish American War was the first time field uniforms were routinely colored to not stand out in theater. The gray-green and browns were not too far from much of Northern Mexico... WW I you get the Zebra Dazzle on ships, and the khakis for US, UK, and French soldiers, and the Feldgrau for Deutschland.
If you want to see the effects of even that level of camouflage, I'll recommend the movie
1917... period correct (or very close) uniforms. Right colors of mud and fields...