Heat broiler or grill.
In large bowl, work together ground chuck, onion flakes, salt and pepper until well blended. Shape into 6 equal patties.
Broil or grill 4 to 6 inches from heat 5 minutes. Turn over and broil or grill another 5 to 6 minutes or until internal temperature registers 145 degrees F on instant-read thermometer for medium (temperature will increase to 155 degrees F).
Meanwhile, in large skillet, cook chopped bacon over medium-high heat until fat is rendered and bacon is almost crispy, 3 to 4 minutes. Add mushroom slices; cook until softened, about 3 minutes. Sprinkle with flour; cook, stirring, 1 minute. Pour in beer and Worcestershire. Reduce heat to medium; simmer, stirring occasionally, until some of liquid evaporates, 4 to 5 minutes.
While sauce is simmering, top each burger with a slice of cheese. Place under broiler or on grill and cover; melt cheese, about 1 minute. Split each pita in half horizontally (making 6 rounds); toast, if desired.
To serve, place 1 cheeseburger on top of each pita round. Top with 2 to 3 tablespoons mushroom-bacon sauce and serve with coleslaw on side. Makes 6 servings.
In large bowl, stir together coleslaw mix, mayonnaise, vinegar, sugar and mustard powder until well blended. Refrigerate at least 1/2 hour before serving.