Preheat the oven to 375 degrees F (190 degrees C).
Bring rice and water to a boil in a saucepan. Reduce the heat to medium-low, cover, and simmer until the rice is tender and the liquid has been absorbed, 45 to 50 minutes.
Heat olive oil in a skillet over medium-low heat; cook and stir green onions and garlic until fragrant, 1 to 2 minutes.
Add artichoke hearts, tomato, basil, red pepper flakes, and black pepper. Cook and stir artichoke mixture until heated through, about 5 minutes. Stir in rice and remove from heat.
Crumble about 1 teaspoon feta cheese into the bottom of each red bell pepper. Spoon rice mixture into each red bell pepper to fill halfway. Crumble another teaspoon feta cheese over filling; top with more filling.
Place red bell peppers in a glass baking dish.
Bake in the preheated oven until feta cheese has melted and red bell peppers are slightly tender, about 15 minutes.