What spices goes into Fajita spice mixture?

Sounds like the ingredients in a pre-mixed packet. Oregano would make sense, onion powder too. Cornstarch is probably there to make a coating that protects the chicken cutlet from direct heat. But, you could also try briefly marinating in a lime-juice, olive oil, salt, pepper, and fresh minced garlic marinade for maybe half an hour; you could spice it up with a little optional chili powder, cumin and oregano. Lift out of the marinade and pat dry with paper towels, then "grill" on a ridged grill pan, then slice.
Something I've been doing lately when I have leftover, cooked chicken that is similar, now that I think about it: Sauté sliced red bell pepper in olive oil in a large nonstick pan, after a couple minutes add sliced onion. When they are translucent, add cooked chicken, taken off the bone and shredded, to the mixture, just to warm it. Add the seasonings mentioned above (or, just good-quality smoked Spanish paprika), give it a stir to distribute the spices; you can add a couple splashes of water to moisten it, cook it a few minutes longer to reduce the water and concentrate the flavors. You could serve that in warmed tortillas. My family loves this, even when it's leftovers. Easy and delicious.

oops, I see I didn't read carefully enough and you are making chicken. You can certainly try a spice rub with the spices and herbs you mentioned. Start with a tablespoon or so of chili powder to about 1/2-1 teaspoon of cumin, add 1/2 teaspoon of garlic powder, salt and pepper, rub it into cutlets for a dry marinade and let sit about an hour or two (or overnight), refrigerated, cook on a ridged grill pan or a hot iron skillet with about a tablespoon of oil (or grill).