Mix all the marinade ingredients in a large bowl, except for the meat itself.
Blend the marinade with a hand blender or in a blender or food processor.
Mix in the meat and allow to marinate for a few hours.
Grill the meat to medium.
Allow to rest before slicing against the grain.
Stretch out the bread to the long and thin shape known for flatbread.
Toss the zucchini, bell pepper, and kale with some oil and salt.
Grill the veggies on high heat to brown. Remove from heat.
Brush the bread with olive oil. Grill to brown on both sides. Remove from heat and turn the grill to low.
Build your flatbread adding the zucchini, peppers, kimchi, and meat. Top with the cheese.
Place on the grill and close the top to let the cheese melt, about 5 minutes. Keep an eye on it because if the grill is still hot it might burn. I moved mine to the top rack after a few minutes.
Remove from the grill and top with the kale. Slice and serve.