Heat 1 tablespoon oil in large nonstick skillet over medium-high heat. Add onion; sauté until beginning to soften, 3 minutes. Add bell pepper, 1 1/2 teaspoons thyme, and garlic; sauté 1 minute. Add beans; sauté until just beginning to soften, about 3 minutes. Add zucchini; sauté until all vegetables are crisp-tender, 4 minutes longer. Stir in corn; remove from heat.
Cover cutting board with large sheet of plastic wrap. Arrange chicken, smooth side up, on plastic wrap, spacing several inches apart. Sprinkle with remaining 3 teaspoons thyme, then pepper. Place 1 ham slice on each chicken breast, trimming so edges extend slightly over chicken. Place another sheet of plastic wrap atop chicken breasts. Using meat mallet or rolling pin, pound evenly to scant 1/2-inch thickness. Turn chicken over and sprinkle lightly with salt and pepper, then flour.
Heat 2 tablespoons oil in each of 2 heavy large skillets over medium-high heat. Divide chicken between skillets, ham side up, and cook until edges of chicken begin to turn opaque, about 4 minutes. Turn chicken over and cook until cooked through, 4 minutes longer. Remove from heat; cover.
Rewarm succotash over medium-high heat, stirring constantly. Mix in cream; season with salt and pepper.
Transfer chicken to plates, ham side up. Spoon succotash alongside.