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Electricity markets differ in their ability to meet power imbalances in short notice in a controlled fashion. Relatively flexible markets have the ability to ramp up (or down) power flows across interties without compromising their ability to reliably meet internal demand. In this paper, a market mechanism to enable flexibility trading amongst market operators is introduced. In the proposed market mechanism, market operators exchange information regarding optimal terms of trade (nodal prices and flows) along interconnection lines at every trading round. Equipped with this information, each market operator then independently solves its own internal chance-constrained economic dispatch problem and broadcasts the updated optimal terms of trade for flows across markets. We show the proposed decentralized market mechanism for flexibility trading converges to a Nash equilibrium of the intraday market coupling game, i.e. a combination of internal market clearing solutions (one for each participating market) and flows and prices along interconnection lines so that no individual market operator has an incentive to modify its own internal solution and/or the terms of trade along interties. For a specific class of chance constraints, we show that the limiting equilibrium outcome is efficient, i.e. it corresponds to the solution of the single market clearing problem for all participating markets. The proposed market mechanism is illustrated with an application to the three-area IEEE Reliability Test System.