Pound the chicken thigh fillets with a meat mallet to flatten lightly. Purée the kimchi, lime juice and sesame oil, then toss with the chicken and set aside.
Mix the zucchini, mint, garlic and chilli flakes, then season lightly with salt and pepper. Pound the black sesame seeds in a mortar, then mix with the aioli and chives.
Cook the chicken fillets on a hot barbecue grill for 5 minutes, basting with the marinade from time to time. Put the cheese slices on top to melt.
Arrange the zucchini salad on the burger base, then the chicken pieces and aioli.