In a large zip-top bag, combine soy sauce, garlic, honey, ginger and pepper flakes. Add steak, seal bag and turn to coat. Marinate in refrigerator for 1 to 4 hours.Cook rice according to package directions.Meanwhile, fill a separate saucepan halfway with water and bring to a simmer. Add spinach and cook until wilted, 1 minute. Drain spinach in a colander, pressing to remove as much moisture as possible. In a medium bowl, toss spinach with oil and salt; set aside. In a small bowl, toss carrots with vinegar; set aside.Heat a grill pan on medium-high. Remove steak from bag, discarding marinade. Grill steak to desired doneness, 4 to 5 minutes per side for medium rare. Transfer steak to a cutting board, cover loosely with foil and let rest for 10 minutes. Using a serrated knife, thinly slice against the grain.Mist a medium nonstick skillet with cooking spray and heat on medium. Cook eggs over easy, until whites are set and yolks are still runny.Divide rice among bowls. Place steak, spinach, carrots and kimchi in small mounds over rice. Place 1 cooked egg in each bowl and sprinkle with onions.