Prepare a medium fire in a charcoal grill with a cover, or preheat a gas grill to medium.
For the mayonnaise:
Combine the oil and garlic in a small, fire-proof saucepan on the grill and cook for 1 minute. Add the wine and saffron and heat, stirring occasionally and using the back of a spoon to crush the saffron and help release the color, until the mixture is reduced and thickened, about 10 minutes. Transfer to a small bowl and set aside to cool.
When the saffron mixture is cool, add the mayonnaise and stir to blend. Cover and chill until ready to use.
For the patties:
Slice the chorizo and pulse in a food processor to chop. Transfer to a large bowl. Add the oil, garlic, wine, saffron threads, onion, sweet pepper, salt, black pepper, bread crumbs, and egg and mix well. Coarsely chop the shrimp and add to chorizo mixture. Add the ground chicken and mix gently. Shape into 6 patties to fit the rolls.
Put the onion and pepper slices on a baking sheet or platter and brush with the oil. Sprinkle with the salt and pepper.
When the grill is ready, rub the grill rack with oil. Place the patties on the grill and cook for 6 minutes per side, until cooked through, being careful not to overcook. Grill the onion and pepper slices until crisp-tender and showing grill marks, about 1 minute per side for the peppers and 3 minutes per side for the onion. While they are cooking, toast the rolls.
To assemble the burgers:
Spread the toasted sides of the rolls with the mayonnaise. Place a patty on the roll bottoms, then add the grilled onion and red peppers, dividing evenly. Top with the tomato slices and the roll tops.
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