We study a stochastic Cucker-Smale flocking system in which particles interact with the environment through white noises. We provide definition of flocking to the stochastic system, and show that when the communication rate is constant, the system exhibits a flocking behavior independent of the initial configurations. For the case of a radially symmetric communication rate with a positive lower bound, we show that the relative fluctuations of the particle velocity around the mean velocity have a uniformly bounded variance in time. We conclude with numerical simulations that validate our analytical results.