In a large bowl, combine the shredded chicken and basil pesto. Mix until the chicken is well coated.

Add the diced avocado, crumbled bacon, cherry tomatoes, red onion, and mixed greens to the bowl. Gently toss to combine. Season with salt and pepper to taste.

Lay out the flour tortillas on a clean surface. Spoon an equal amount of the chicken and avocado mixture onto the center of each tortilla.

Fold in the sides of the tortilla and then roll it up tightly from the bottom to the top.

Slice each wrap in half diagonally and serve immediately, or wrap in foil and refrigerate for up to 2 hours before serving.