Heat grill to medium heat.
Drizzle milk over bread in medium bowl; let stand 2 min. Add chicken; mix just until blended. Shape into 4 (1/2-inch-thick) patties.
Grill 5 to 7 min. on each side or until done (165°F). Meanwhile, mix cream cheese and blue cheese until blended.
Spread cut sides of buns with cheese mixture. Place burgers on bottom halves of buns; brush with Wings Sauce. Top with celery; cover with tops of buns.