Preheat oven to 350 degrees. Line a cookie sheet with a cooling rack.
If you're using four small chicken breasts, place each chicken breast on a cutting board and place a large piece of plastic wrap on top. Use a meat mallet or rolling pin, to slightly flatten each chicken breast. If you're using two large chicken breasts, use a sharp knife to cut each breast in half, lengthwise, repeat process to slightly flatten chicken.
Add flour and 1/4 teaspoon salt to a shallow dish, whisk to combine. Add egg and 2 tsp water to another shallow dish, whisk to combine. Add potato flakes, breadcrumbs, 1/2 teaspoon salt and garlic powder to another shallow dish. Whisk to combine.
Season chicken breasts with salt and pepper on both sides. Dredge one chicken breast in flour, pat off any excess flour. Coat both sides of chicken in egg mixture, let any excess egg drip off. Finally, coat each chicken breast in potato flake mixture, making sure to press into the chicken. Set aside, and repeat with remaining three chicken breasts.
Heat two large non-stick skillets to a medium heat. Once the pan is hot, add 1 tablespoon butter and 1 tablespoon olive oil to each pan. Once the butter has melted and the oil is hot, add two chicken breasts to each pan. Cook until golden brown on both sides, about 3-4 minutes per side. Transfer to cooling rack. Pop in the oven while you make the sauce.
Turn the heat off on one pan, and reduce the heat to low on the other. Add white wine to the pan that's still heated. Bring the mixture to a boil and then reduce to a simmer until it's reduce by half, about 2 minutes. Add lemon juice, simmer for another 1-2 minutes. Turn the heat down to low and add butter. Whisk until combined. Add capers and parsley.
Arrange chicken on a platter or plate, spoon sauce on top. Garnish with more parsley if desired.