Adjust oven rack to middle position and heat oven to 425 degrees. Stir cream cheese, goat cheese, dried figs, thyme, garlic, 1/4 teaspoon salt, and 1/4 teaspoon pepper together until smooth.
Pound chicken to even 1/4-inch thickness. Pat dry with paper towels, then season with salt and pepper. Following photos, mound 1/4 cup of cream cheese filling at wider end of chicken, form cheese into log, and then roll chicken up. (You will have some leftover filling.)
Arrange chicken rolls, seam-side down, about 1/2 inch apart in 13- by 9-inch baking dish coated lightly with vegetable oil spray.
Mix any remaining cream cheese filling with mayonnaise, mustard, and lemon juice, then brush mixture over tops and sides of chicken. Toss breadcrumbs with butter, then press onto tops and sides of chicken rolls.
Bake until breadcrumbs are golden and very center of chicken rolls registers 160 degrees on instant-read thermometer, about 30 minutes. Serve with lemon wedges.