Do some prep: Cut 1 pint of Sungold tomatoes in half. Thinly slice 8 garlic cloves, 1 shallot, and 1 Fresno chili or jalapeno. Coarsely chop 1 tablespoon capers. Set all these ingredients aside, somewhere near the stove.
Pound and dredge the chicken: Place a boneless skinless chicken thigh between two pieces of parchment. Pound the chicken out until about ½” thick all around. Season the chicken thighs all over with salt and pepper. Dredge each chicken thigh in 1 cup flour and transfer to a plate.
Cook: Heat 2 tablespoon olive oil in a large cast iron skillet until very hot. Cook the chicken thighs until deeply golden brown underneath, 3-4 minutes. Flip and cook 30 seconds longer. Transfer cooked chicken to a plate and repeat with remaining thighs. Reduce heat, add 1 tablespoon butter, garlic, chilies, shallot, and capers. Cook until garlic begins to turn golden, 1-2 minutes. Add ⅓ cup wine and cook until mostly evaporated. Stir in ½ cup water, 3 tablespoons butter, half of the sliced tomatoes, basil, and salt. Simmer until sauce reduces and thickens, 5-8 minutes. Return chicken to skillet with remaining tomatoes and heat through.
Serve: Stir the juice of one lemon into the skillet. Taste the sauce and adjust seasoning as needed. Serve right out of the skillet.
