Place chicken legs into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until no longer pink at the bone, 15 to 20 minutes. Drain and let cool. Shred chicken meat and season with salt.
Heat oil in a large skillet over medium heat. Cook and stir onion until soft, about 5 minutes. Add mushrooms and cook until soft, 5 to 8 minutes.
Mix mayonnaise and garlic together in a bowl. Mix 1/4 cup of the mayonnaise with the chicken.
Spread chicken-mayonnaise mixture in the shape of a disk on a serving plate. Cover with onion-mushroom mixture and 1/4 cup of mayonnaise. Add grated egg whites and 1/4 cup of mayonnaise. Sprinkle Cheddar cheese on top; cover with remaining mayonnaise. Sprinkle grated egg yolks evenly over the top.
Cut olives into 4 wedges each and place on top to resemble sunflower seeds. Refrigerate salad for 2 hours.
Place potato chips around the salad to resemble sunflower petals.