Corona Renderer currently ignores motion blur settings of FumeFX nodes.

See: Corona Renderer no longer supports FumeFX

Motion blur can be toggled in the FumeFX UI > rend tab Motion Blur.

Motion blur of the volume data is currently ignored (blur caused by the movement of fire or smoke particles, etc.), however standard motion blur does work - for example if the FumeFX node is translated, scaled, or rotated. 

See also: Volumetric FX - Known bugs and limitations