Mix flour, baking powder, and salt together in a large bowl. Pour in water; stir dough until just combined. Cover with plastic wrap and let rest, about 15 minutes.
Heat a large skillet over medium heat. Add ground beef; cook and stir until browned, about 5 minutes. Drain off grease. Stir in pinto beans, diced tomatoes with their juices, and chili seasoning until well-blended. Simmer until chili flavors combine, 10 to 15 minutes.
Grease your hands lightly with oil and pinch off a piece of dough about the size of a baseball. Press it with your palms into a round about 4 inches in diameter and 1/2-inch thick. Repeat with remaining dough.
Heat oil to a depth of 2 to 3 inches in a deep fryer or large saucepan. Fry dough rounds in batches until well-browned, puffy, and cooked through, 2 to 3 minutes per side. Drain on paper towels.
Divide fry bread among serving plates while still hot. Spoon chili mixture on top.
