  The black hole spacetime is described by general relativity and characterized
by two quantities: the black hole mass and spin. Black hole spin measurement
requires information from the vicinity of the event horizon, which is spatially
resolved for the Galactic center SagittariusA* (SgrA*) and nearby radio galaxy
M87 by means of very long baseline interferometry (VLBI) observations with the
Event Horizon Telescope (EHT). In this paper, we simulate EHT observations for
a gas cloud intermittently falling onto a black hole, and construct a method
for spin measurement based on its relativistic flux variation. The light curve
of the infalling gas cloud is composed of peaks formed by photons which
directly reach a distant observer and by secondary ones reaching the observer
after more than one rotation around the black hole. The time interval between
the peaks is determined by a period of photon rotation near the photon circular
orbit which uniquely depends on the spin. We perform synthetic EHT observations
for SgrA* under a more realistic situation that a number of gas clouds
intermittently fall towards the black hole with various initial parameters.
Even for this case, the black hole spin dependence is detectable in correlated
flux densities which are accurately calibrated by baselines between sites with
redundant stations. The synthetic observations indicate that our methodology
can be applied to EHT observations of Sgr A* since April 2017.
