Make lemon herb butter: Melt butter in a small saucepan over medium heat. Add garlic, lemon zest, 3 Tbsp chopped dill and pepper flakes (if using). Cook until fragrant, about 3 minutes. Remove pan from the heat and let cool. Discard garlic.
Cut off ends of zucchinis. Using a mandoline equipped with a finger guard, thinly slice each zucchini lengthwise. (slices should be thickness of a quarter.) Lay slices flat on a rimmed sheet pan. Lightly brush slices on both sides with lemon herb butter and season with salt and pepper.
Fold a zucchini slice into an accordion shape and thread onto a flat skewer. Don’t worry if a few of the slices break—skewer the pieces back to back. If using round bamboo skewers, insert a second skewer parallel to the first. (This keeps the zucchini slices from spinning.) Slice, butter, season and skewer remaining zucchini. You should wind up with 8 kebabs.
Set up your grill for direct grilling and heat to high. Arrange kebabs, skin side down and grill until darkly browned at the edges, 3 to 4 minutes. Turn and grill other side skin side down the same way, 6 to 8 minutes in all. Baste skewers with lemon herb butter as they grill. Transfer to a platter or plates for serving and spoon any remaining butter over them.