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Understanding and predicting how influenza propagates is vital to reduce its impact. In this paper we develop a nonparametric model based on Gaussian process (GP) regression to capture the complex spatial and temporal dependencies present in the data. A stochastic variational inference approach was adopted to address scalability. Rather than modeling the problem as a time-series as in many studies, we capture the space-time dependencies by combining different kernels. A kernel averaging technique which converts spatially-diffused point processes to an area process is proposed to model geographical distribution. Additionally, to accurately model the variable behavior of the time-series, the GP kernel is further modified to account for non-stationarity and seasonality. Experimental results on two datasets of state-wide US weekly flu-counts consisting of 19,698 and 89,474 data points, ranging over several years, illustrate the robustness of the model as a tool for further epidemiological investigations.