If working with one large chicken breast, butterfly the chicken first. See Notes. Season the chicken breasts on all sides with the Greek seasoning, and let it sit at room temperature for about 10-15 minutes before cooking.
Heat the olive oil in a large pan over medium heat. Cook the chicken for about 3-4 minutes per side, until browned and cooked through. Transfer to a cutting board for about 5 minutes to slightly cool, then shred it apart or cut into small pieces.
Toss the shredded kale with the Mediterranean vinaigrette. Season with salt and pepper, if desired.
Warm the mini naan flatbreads in a dry pan over medium heat for about 30 seconds per side, or about 20 seconds total in the microwave.
Spread one tablespoon of hummus onto each mini flatbread. Divide the thinly sliced red onion, kale, shredded chicken, and crumbled feta over each one. Fold in half (like a "taco"), and enjoy!