Place porcini mushrooms in a small bowl; cover with boiling water. Cover and let stand 30 minutes or until tender. Drain and rinse; drain well. Thinly slice.
Place each chicken breast half between 2 sheets of heavy-duty plastic wrap; pound chicken to 1/2-inch thickness using a meat mallet or small heavy skillet. Combine 3 teaspoons flour, 1/4 teaspoon salt, and black pepper in a shallow dish. Dredge chicken in flour mixture.
Heat a large stainless steel skillet over medium-high heat. Add 1 tablespoon oil to pan; swirl to coat. Add chicken; cook 3 minutes on each side or until done. Remove from pan; cover and keep warm.
Heat remaining 1 tablespoon oil in pan over medium-high heat. Add onion, red pepper, and garlic; sauté 2 minutes or until onion is lightly browned. Add remaining 1/2 teaspoon salt, porcini, shiitake, button mushrooms, and oregano; sauté 6 minutes or until mushrooms release moisture and darken. Sprinkle with remaining 1 teaspoon flour; cook 1 minute, stirring constantly. Stir in wine; cook 1 minute. Add broth; bring to a boil. Reduce heat, and simmer 1 minute. Add chicken and tomatoes; cook 2 minutes or until thoroughly heated, turning chicken once. Sprinkle with basil.