Place chicken between 2 sheets of plastic wrap or parchment paper and use a frying pan to gently pound the breasts to an even thickness. (They should be about 1 inch thick.)
Combine flour, salt, and freshly ground black pepper in a wide, shallow dish and mix thoroughly. Coat each breast by dredging it in the flour mixture then shaking off excess flour. Wrap one piece of bacon around each piece of chicken and secure with a toothpick.
Heat oil in a medium, heavy-bottomed frying pan over medium heat. When it shimmers, add chicken breasts and cook until bacon is well browned, about 5 minutes per side.
Add the juice, reduce heat to medium-low, and simmer until cider is reduced by 1/3, and chicken is cooked through, about 5 minutes more. Remove from heat and remove toothpicks.
To make a sandwich, spread mustard evenly on cut sides of bread. Layer half of each endive and apple slices alternately on one piece of bread, top with a chicken breast, drizzle with pan juices, season with freshly ground black pepper, and close sandwich. Repeat to make a second sandwich.