Preheat the oven to 300°F (150°C). Grease a large baking pan with sides.

Combine beef, lamb, flour, oregano, salt, dry mustard, garlic powder (2 ½ tsp), black pepper, cayenne pepper, chili pepper, paprika, and Italian seasoning in a bowl; knead with hands until mixture is paste-like, about 10 minutes. Roll into a large loaf shape and place into the prepared baking pan.

Bake in the preheated oven until no longer pink in the center, about 2 hours. An instant-read thermometer inserted into the center should read at least 160°F (70°C). Remove from oven; let the loaf cool completely on a drip rack to drain juices and fat. Refrigerate for 6 hours or overnight.

Make the sauce: Combine evaporated milk, sugar, and garlic powder in a small bowl. Gradually stir in vinegar until the mixture thickens.

Slice the donair loaf into strips about 1/8 to 1/4-inch thick. Fry the slices in a skillet over medium-high heat until they begin to crisp at the edges. Rub a pita round lightly with water and fry in the same skillet until warm.