Begin by gathering all the required ingredients.
In a slow cooker, combine the steak sauce, bouillon cubes, kosher salt, freshly ground black pepper, sugar, and hot water or stock. Stir the mixture well to ensure the flavors are thoroughly blended.
Add the boneless chicken thighs, lean stewing beef cubes, chopped onion, peeled and cubed potatoes, thinly sliced carrots, and the can of stewed tomatoes to the slow cooker. Gently stir the ingredients to evenly distribute the flavors.
Cover the slow cooker and set it on the low setting for 8 to 10 hours or on the high setting for approximately 5 hours. This slow cooking process will allow the flavors to meld and intensify.
Around the halfway mark of the cooking time, carefully remove the boneless chicken thighs. Chop the chicken into bite-sized pieces and return the chopped meat to the slow cooker. Give the mixture a good stir to incorporate the chicken.
Create a smooth paste by mixing the all-purpose flour with 1/4 cup of cold water. Gradually stir this flour mixture into the stew in the slow cooker. Continue cooking on the high setting for approximately 15 to 20 more minutes, or until the stew reaches the desired thickness.
Serve this hearty chicken and beef stew alongside warm biscuits, cornbread, or crusty bread for a wholesome and satisfying meal.