Rapid growth in data centers and other large loads is straining transmission grid interconnection processes. This paper develops a framework to quantify firm transmission grid capacity and additional risk-aware flexible capacity that can be unlocked when large loads accept a predefined level of interruption risk. We design a normalized unmet-request objective to serve large load requests. We prove that, in radial networks, every minimizer of this objective also maximizes aggregate interconnected capacity, and we show numerically that this property nearly holds on meshed networks. To allocate the firm and flexible transmission capacities among competing large loads, we use a simultaneous ascending auction (SAA) over products differentiated by {\em capacity, risk level, and bus location}. When large loads have additive, symmetric concave, unit-demand, and $K_b$-demand valuations of the firm and flexible capacity products, we show that the gross substitutes property holds, which supports SAA convergence to a competitive equilibrium. A numerical study on the IEEE 73-bus system shows that, at a 1\% risk setting, flexible capacity increases the total network capacity by 44.3\% relative to the firm capacity baseline, while the SAA reaches a competitive equilibrium.

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