Make the marinade by whisking together the olive oil, lemon juice, red wine vinegar, minced garlic, oregano, and a pinch of crushed red pepper to taste in a zip-lock bag. Add the chicken breasts and marinate in the refrigerator for 1 hour.
Remove chicken from the zip-lock bag and place it on a plate. Season both sides with sea salt and freshly cracked pepper, to taste.
Cook the chicken by preheating a grill pan coated with olive oil cooking spray over medium heat.
Place the seasoned chicken in the grill pan and cook for 8-10 minutes. Flip the chicken over and cook for an additional 7-8 minutes, or until the chicken has cooked through.
Allow the chicken to rest for a few minutes on a cutting board before slicing it into thin strips.
Warm pita bread (or flatbread) in the microwave for 20 seconds.
To serve, top the pita with the tzatziki sauce, sliced chicken, mixed greens, tomatoes, red onion, and feta cheese.