The tendency of a substance to burn with rapid and sparkling combustion is known as:

The tendency of a substance to burn with rapid and sparkling combustion is accurately described by deflagration. This term refers to a type of combustion that occurs at a rate less than the speed of sound in the material, characterized by the production of flames and often accompanied by a specific visual effect, including sparking. Deflagration typically involves the rapid oxidation of a fuel that generates heat and light, which can lead to an explosive reaction when confined, but does so in a way that doesn't produce the shockwave associated with detonation.

In contrast, detonation involves a violent reaction that occurs at a speed exceeding that of sound, resulting in a shockwave. Combustion is a broader term that encompasses all types of burning, with or without rapid burning characteristics. The flash point is the lowest temperature at which a substance can vaporize to form an ignitable mixture in air but doesn't specifically address the behavior of combustion described in the question.

Thus, the characteristics of deflagration align precisely with the rapid and sparkling combustion described, making it the best choice in this context.