Diamond is a form of carbon and it will burn to form carbon dioxide. I
know that heats of combustion have been measured in pressurized oxygen
atmospheres. I do not know if a normal fire will produce the conditions
to cause it to burn.

Greg Bradburn
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Strictly speaking, diamond is not flammable, but it is combustible.
"Flammable" basically means that something burns with great intensity. I
have never personally seen diamond burn, but it can happen.I don't know how
hot you need to make it to ignite it.

Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois