No, ethidium bromide is not flammable, nor combustible. However, hazardous combustion products may arise from the substance or mixture such as carbon oxides, nitrogen oxides (NOx), and hydrogen bromide gas.
In case of a fire, extinguish it using water spray, carbon dioxide, dry chemical or alcohol-resistant foam. Wearing special protective equipment such as self-contained breathing apparatus while fighting a fire in the proximity to EtBr is crucial to avoid accidental exposure to ethidium bromide.