Combine oil, wine, lemon juice, vinegar, salt, pepper, thyme, oregano, tarragon, red pepper flakes, and cayenne pepper in a bowl. Stir in onion and garlic. Add chicken cubes last; coat thoroughly.

Pour mixture into a resealable freezer bag, making sure there is as little air as possible in the bag. Wrap bag in a paper towel and slide it into another resealable bag so that the zippers are at opposite ends. Refrigerate, flipping over every 12 hours, for 2 to 3 days.

Soak wooden skewers in water. Thread the chicken cubes through the skewers, discarding marinade.

Preheat an outdoor grill for medium-high heat and lightly oil the grate. Grill the chicken skewers, flipping halfway, until juices run clear, 8 to 10 minutes.