The space-time correlation functions of amplitude and intensity fluctuations are derived for a dynamic speckle generated by a flat diffuse object illuminated with a TEM10 Hermite- Gaussian laser mode. The object is assumed to move in a plane with a constant velocity. The considerations are limited to the free propagation geometry. The speckle complex amplitude is assumed to obey circular Gaussian statistics. It is shown that intensity fluctuation is a space- time stationary process and its correlation function derived for both near and far diffraction fields depends on the angle which forms the vector of velocity and one of the axes of symmetry of the TEM10 laser mode. This enables the simultaneous measurement of the direction and the magnitude of the object velocity. The velocimetry formulae are derived for a boiling far field speckle detected with a single point detector or with a circularly symmetric soft Gaussian aperture.