Preheat grill to 400 degrees F.
Into a large mixing bowl, add vegan mayonnaise, vegan Parmesan cheese, garlic, sea salt, ground black pepper, onion powder, paprika, and red pepper flakes Stir to combine.
To the mayonnaise and spice mixture, add the thinly sliced potatoes.
Toss gently to thoroughly coat the potato slices.
Adjust seasoning to taste.
Arrange foil squares with the non-stick side facing up.
Divide the potato mixture evenly between the foil squares.
Fold the aluminum foil over the potatoes, crimping the open ends to form a packet.
Place on the grill over indirect heat. Make sure the packets are not touching to allow for heat to circulate all around.
Close the lid and cook 30 minutes.
Remove from the grill then carefully open the packets.
Serve hot.