We present a Buildings-to-Grid (BtG) integration framework with intermittent wind-power generation and demand flexibility management provided by buildings. First, we extend the existing BtG models by introducing uncertain wind-power generation and reformulating the interactions between the Transmission System Operator (TSO), Distribution System Operators (DSO), and buildings. We then develop a unified BtG control framework to deal with forecast errors in the wind power, by considering ancillary services from both reserves and demand-side flexibility. The resulting framework is formulated as a finite-horizon stochastic model predictive control (MPC) problem, which is generally hard to solve due to the unknown distribution of the wind-power generation. To overcome this limitation, we present a tractable robust reformulation, together with probabilistic feasibility guarantees. We demonstrate that the proposed demand flexibility management can substitute the traditional reserve scheduling services in power systems with high levels of uncertain generation. Moreover, we show that this change does not jeopardize the stability of the grid or violate thermal comfort constraints of buildings. We finally provide a large-scale Monte Carlo simulation study to confirm the impact of achievements.