A match-head is flammable, but you have to get it up to its ignition temperature first.
A diamond is flammable, but its ignition temperature is astronomical and totally out of sight.
Diamonds are not flammable, but are combustible, when a diamond burns there is no ash because diamonds are pure carbon and when burned it is turned into carbon dioxide. :D
Diamonds can burn, but they are not flammable in the usual sense because their ignition temperature is very high (around 700 °C or 1292 °F). They are stable under typical conditions and require extreme temperatures to ignite. Therefore, they are not easily combustible like many other materials.
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