In a large pot of boiling, generously salted water, cook green beans, stirring occasionally, until bright green and crunchy, 2 to 3 minutes. Using tongs or a slotted spoon, transfer beans to a large bowl of ice water. Drain and pat dry.
Meanwhile, cut kernels off corn cobs and transfer kernels to a medium microwave-safe bowl. Microwave in 30-second increments, stirring between each, until slightly softened, about 90 seconds total.
In a food processor, pulse parsley, oil, cilantro, oregano, garlic, lemon zest, lemon juice, vinegar, red pepper flakes, and 1 tsp. salt until smooth.
Transfer chimichurri to a large bowl. Add green beans, shallot, corn, and feta and toss to combine.