Arrange bok choy and red pepper in bottom of slow cooker. Season 4 chicken breast halves all over with salt and black pepper and place on top of bok choy.
In a small bowl, whisk together broth, sake, sesame oil, ginger, and curry paste. Pour mixture over chicken. Cover and cook on LOW for 6 to 8 hours or HIGH for 3 to 4 hours.
In a small skillet toast flaked coconut on low heat until lightly toasted, about 5 to 8 minutes. To a medium saucepan, add rice and coconut milk and set pan over medium-high heat, bring to a simmer for 5 minutes. Remove from heat and let stand 5 minutes. Stir in toasted coconut. Set aside 1 1/2 cups for another recipe.
Spoon rice onto a serving platter. Top with chicken, bok choy, bell peppers and sauce from slow cooker. Garnish with cilantro.