Three main factors are chemistry, surface area, and oxidant levels.
A burning reaction in chemistry is typically referred to as a combustion reaction (unsurprisingly) with some chemical bonds have more energy (read more likely) to sustain the reaction after breaking.
Increased surface area, like dust, increase the amount of material exposed to heat and as a result is easier to burn
All combustions require an oxidant (like oxygen) which is essentially an electron hungry chemical
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