In a small pot fitted with a deep-fry thermometer, heat 2 cups of oil to 350 degrees. Toss shallots with flour and shake to remove excess. Fry shallots in batches, stirring occasionally (but especially within the first 30 seconds of adding them to the pot) to prevent them from sticking to each other. When shallots begin to turn a light golden brown, about 6 minutes, remove them to a paper towel-lined plate to drain. Salt immediately and generously.
In a small pan over medium-high heat, toast pistachios until fragrant, about 5 to 7 minutes. When cool enough to handle, chop roughly and set aside.
Set oven to broil. Using 1 tablespoon of oil, gloss ears of corn with a sheer coat, season generously with salt and pepper, and place on a rimmed baking sheet. Broil corn until lightly charred, about 10 minutes, turning once. Remove from oven. When cool enough to handle, cut kernels from cob and set aside.
In a medium bowl, whisk together vinegar and remaining 2 tablespoons of oil. Toss dressing with radicchio, corn, pistachios, and a generous pinch of salt. Top with shallots.