Place ground beef in the pressure cooker over medium-high heat; cook until brown and crumbly, 8 to 10 minutes. Remove beef; drain off excess fat.
Heat olive oil in the pressure cooker over medium heat; stir in onion, green pepper, and jalapeño. Cook and stir until onion has softened, about 3 to 4 minutes. Add garlic; cook and stir for about 30 seconds. Stir in browned beef, diced tomatoes, kidney beans, water, tomato paste, chili powder, brown sugar, cocoa powder, cumin, salt, and red pepper flakes.
Lock the lid, bring the cooker up to pressure, reduce heat to maintain pressure, and cook for 8 minutes. Remove the cooker from the heat, and let the pressure reduce on its own, 5 to 10 minutes.
When the pressure is fully released, remove the lid, stir the chili and serve.