Whisk mayonnaise, yogurt, and chipotle chiles together in a bowl.

Cook tortillas in the microwave until warm and pliable, about 30 seconds.

Spread 1 tablespoon chipotle mayonnaise down the center of each tortilla. Spread 1/2 of the lettuce, 1/2 of the Monterey Jack cheese, 1/2 of the avocado, 1/2 of the bacon, 1/2 of the red onion, 1/2 of the tomato, and 1/2 of the chicken, respectively, in the center of each tortilla. Fold opposing edges of tortilla to overlap the filling. Roll 1 of the opposing edges around the filling into a wrap.