The tart, oily flavors of aleppo brighten chicken's mild taste, and act as a nice counterpart to the dark, super-savory flavors of grilling. Chiles burn if exposed to direct heat for too long, so whisk some aleppo into a basting sauce and brush on during the end of cooking.
The hot, pungent flavor of mustard seeds is unleashed only when they cook over high heat and pop open. In other words, they're perfect for grilling. Mustard seeds take well to a range of flavors: cumin, coriander, chiles, soy and hoisin, or green onions. Take mustard seed as a base flavor and customize away.
The earthy, spicy, crazy complex Ethiopian berbere most famously accompanies chicken in the country's national dish: doro wat. But berbere's great for grilling as well as braises. The raw pungency of the spice will be replaced by roasted, caramelized flavors—sheer magic on chicken in a dry rub before grilling.
When you slowly dry peppers over fragrant wood fires, you get pimentón, one of the world's great spices. It's smoky, sweet, and hot in a restrained way all at once. When you roast those peppers on a chicken's fatty skin over open flame...you get the idea. It's ridiculous. I like paprika most as part of a garlicky marinade for chicken before it meets the grill. Just dry the skin thoroughly before grilling.
You may not think of turmeric as grill-fodder, but you should. It's earthy, rich, and lightly fragrant, and it won't overwhelm the chicken. Coat your chicken in yogurt mixed with turmeric and garam masala for a tandoori-style preparation that forms a fantastic crust.