Cut bell peppers into 2 x 2 1/2-inch strips. Heat 2 teaspoons olive oil in a large nonstick skillet over medium-high heat. Add peppers; sauté 8 minutes. Add raisins; sauté 1 minute. Add 1/4 cup vinegar, sugar, salt, and black pepper; cook 1 minute. Remove from heat; stir in almonds. Set aside, and keep warm.
Place each piece of chicken between 2 sheets of heavy-duty plastic wrap; flatten to 1/4-inch thickness using a meat mallet or rolling pin. Combine breadcrumbs and cheese in a shallow dish. Place flour in a shallow dish; dredge each chicken piece in flour, and dip in egg whites. Dredge chicken in breadcrumb mixture.
Heat 2 teaspoons olive oil in a large nonstick skillet over medium-high heat. Add the chicken, and cook for 3 minutes on each side or until done. Remove from heat. Place the chicken and bell pepper mixture on a serving platter; set aside, and keep warm.
Add 2 tablespoons vinegar and water to pan; stir with a wooden spoon to loosen browned bits. Spoon mixture over chicken and bell pepper mixture.