Spread flour in a shallow dish. Pound the thicker end of the chicken breasts between two sheets of plastic wrap to an even ½-inch thickness. Pat chicken dry with paper towels and season with salt and pepper. Working with one breast at a time, lightly dredge chicken in flour, shaking off the excess.

Heat 1 tablespoon of oil in a 10-inch nonstick skillet over medium-high heat until shimmering. Cook chicken until well browned and registers 160°F, about 6 to 8 minutes per side. Transfer chicken to a serving platter, tent with aluminum foil, and let rest while preparing the relish.

Heat the remaining 1 tablespoon of oil in the same skillet over medium heat until shimmering. Add the corn and cook, undisturbed, until well browned, about 4 minutes. Stir in the garlic and cook until fragrant, about 30 seconds. Stir in the cherry tomatoes and water, scraping up any browned bits. Cook until the tomatoes are just softened, about 2 minutes.

Stir in any accumulated chicken juices, and season the relish with salt and pepper to taste. Spoon the relish over the chicken and sprinkle with avocado and cilantro. Serve with lime wedges.