Preheat oven to 450 degrees, with rack in lowest position. Pat chicken dry with paper towels. Rub skin with butter, and season with salt. Pour out 1/2 cup stout from can; reserve. Poke holes in top of can using a church key. Place thyme in can, and set in a large ovenproof skillet. Place chicken over can, balancing legs to keep it standing like a tripod.
Carefully transfer chicken to oven, breast side first. Roast for 20 minutes. Baste with pan juices. Roast, basting twice, until juices run clear and an instant-read thermometer inserted into the thickest part of a thigh reaches 155 degrees, about 25 minutes more.
Carefully remove skillet from oven. (Steady chicken with 1 hand, using paper towels or mitts to protect your hand.) Let chicken rest (it will continue to cook) until an instant-read thermometer inserted into the thickest part of a thigh reaches 165 degrees, about 10 minutes, then remove from can. Let chicken rest for 10 minutes before serving.
Meanwhile, discard can, and pour pan juices into a cup; skim fat. Return juices to skillet over medium-high heat. Pour in reserved 1/2 cup stout, and bring to a simmer, scraping up brown bits. Mix together water and flour. Whisk into skillet. Boil for 1 minute. Whisk in jam. Simmer until thick, about 2 minutes. Serve chicken with sauce.