Rinse wild rice and place in slow cooker. Add chicken, onion, celery, carrots, broth, and poultry seasoning. Cover and cook on low for about 7 hrs.
When soup has finished cooking, remove chicken and shred with a fork. Return shredded chicken to slow cooker and stir.
Melt butter in a saucepan. Add flour and let the mixture bubble for about 1 minute. Slowly whisk milk into mixture. Add to slow cooker and stir.