Preheat oven to 400F.
While the broiler is heating up, combine cucumbers, tomatoes, vinegar, and 1 Tablespoon olive oil. Season with some salt and pepper. Set aside.
Toss chicken with 1 Tablespoon olive oil, dried oregano, and paprika.
Set flatbreads out in a single layer on a sheet pan. Spread each flatbread with hummus. Sprinkle flatbread with cheese and top with chicken. (Note: I like to put some of the cheese on before the chicken and some after so that you get layers of melted cheese and the chicken gets golden and crisp as it bakes.)
Bake until the edges are golden brown and the cheese is melted, 8 to 12 minutes.
Slice flatbreads and serve with cucumber-tomato salad and tzatziki on top or on the side.
Finish with chopped fresh dill, parsley, or basil.