Whisk soy sauce, honey, sesame oil, ginger, rice vinegar, pepper flakes and garlic in a large bowl. Add shrimp and toss to coat. Refrigerate for 20 to 30 minutes. Remove shrimp from marinade and reserve marinade.
Preheat a grill to medium-high heat.
Prepare 4 large sheets of aluminum foil. Spray each with nonstick cooking spray. Scoop 1/2 cup rice into the center of each sheet. Top each with 1 cup spinach, 1/4 cup zucchini and 1/4 cup snap peas. Divide shrimp evenly among the packets. Spoon remaining marinade over each packet. Fold each packet to close (not too tight), leaving the seam side up.
Place packets, seam-side up, on the grill. Cook until shrimp is cooked through, 12 to 15 minutes. Remove and open packets carefully.