Partially cook short grain brown rice in a rice cooker or saucepan using 1/2 cup less liquid than called for on the package. Cook for about 10 minutes less than the package directs, leaving the rice slightly under-cooked. (If you are using a rice cooker, use the white rice instead of brown rice setting.)
Add tomatoes to the bowl of a food processor or blender pitcher and pulse until nearly pureed, leaving some small pieces; reserve.
Heat olive oil in a large skillet over medium heat. Add shallots; cook and stir until slightly softened, about 2 minutes. Add partially cooked rice; cook and stir to coat with olive oil, about 1 minute. Add warm water and ouzo; stir until absorbed, about 3 minutes. Add pureed tomatoes; cook and stir until tomato has softened and liquid is absorbed, about 3 minutes. Add feta, kalamata olives, and lemon zest; cook and stir until feta has melted, about 1 minute. Add shrimp; cook and stir until shrimp is pink and cooked through, about 3 minutes. Check flavor; add salt and freshly ground black pepper to taste.
Transfer to serving platter and sprinkle with fresh basil and chive flowers if desired. Serve.