Burning Block is a mod that makes fire leave a mark on the world, making it quite obvious where there was a fire. It also means that you might have to clean up after a fire!
Currently the ash block has no uses.
Burning Block is made with modpack and datapack devs in mind: featuring datapack support. Many of the mod's block conversions are controlled by block tags and Neoforge data maps. There is a basic Wiki.
This mod probably doesn't mix with with Burnt, havn't tested it. Burning Block is fully configurable meaning modpack (or datapack) and mod developers can hopefully make whatever blocks/items they are missing out on.
This mod's ash is a decorative block, if you have Supplementaries it will probably spawn both types of ash during a fire. If supplementaries supports the proper item tags both mod's ash should be able to be used in recipes.