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Monk of the Open Hand doesn't need to have been on the battlefield as the first spell was cast. For example, if Monk of the Open Hand is the first spell you cast, and then you cast another spell after the Monk resolved, that spell would cause the Flurry of Blows ability to trigger.

If Monk of the Open Hand is the second spell you cast in a turn, spells you cast after that point in the same turn will not cause the Flurry of Blows ability to trigger.