Combine Dill Pickle Dip Mix, sour cream, mayonnaise and cucumber in a small bowl. Stir well. Chill for 2 hours.
Combine Greek Herb Beer Marinade Mix™ and beer in a resealable plastic bag. Seal and shake to combine. Add chicken, turning to coat. Chill at least 30 minutes.
Preheat grill to medium-high heat. Grill approximately 6-8 minutes per side until no longer pink and internal temperature reaches at least 165°. Cut chicken into bite-sized pieces.
Top each flatbread with dip mixture, chicken, Feta cheese, olives, tomatoes and banana peppers. Fold in half and wrap in fold to serve, if desired.
Use a pie iron and white bread instead of the pita or flatbread.
Make sure the coals are glowing. Grease the insides of the pie iron. Place a slice of bread on one side of the iron. Place a few tablespoons of chicken and toppings on the bread. Top with a slice of bread.
Close the iron; place in the middle of the hottest part of the fire for 2-3 minutes. Turn and cook for an additional 2-3 minutes. The sandwich is done when the sides are toasted and brown.
Use caution when removing the iron from the fire. It will be extremely hot. Allow the sandwich to cool for a few minutes before eating. Serve with dip on the side.