Hydroclimate extreme events, especially precipitation and streamflow, pose serious threats to life, livelihoods, and infrastructure. However, the extremes exhibit significant space-time variability and in conjunction with societal vulnerability and resiliency, resulting in varying levels of damage. Regardless, robust understanding and modeling of these extremes is crucial for effective hazard mitigation strategies. For this study, we focus on the Krishna River Basin in south India, which experiences flooding each year due to monsoon rains and impacts urban and rural communities along its network covering three States. We implement a Bayesian hierarchical model to capture the spatio-temporal variability of streamflow extremes on this river network. In this model, the extremes (3-day maximum seasonal flow) at each station are assumed to follow a Generalized Extreme Value (GEV) distribution with non-stationary parameters. The parameters are modeled as a linear function of suitable covariates. In addition, the spatial dependence of the streamflow extremes is modeled via a Gaussian copula. With suitable priors on the parameters, posterior distribution of the parameters and the predictive posterior distribution of streamflow (i.e., ensembles) at each location. Consequently, various return levels can also be obtained from these ensembles. We developed and tested the model on the monsoon seasonal 3-day max flow at 10-gauge stations for the period 1973 -2015. To find the covariates, we perform analysis to identify relationships between large-scale climate variables such as Sea Surface Temperatures, 850 mb winds, Sea Level Pressure, etc. Statistical learning methods will be employed for this analysis and as a result, obtain potential covariates that best relate to streamflow extremes in the basin. This modeling approach can be adapted to the seasonal and multidecadal projection of extremes, which will greatly help disaster mitigation planning efforts.