Place potatoes, chicken stock, celery, onion, and parsley in a slow cooker; season with salt and black pepper. Cover slow cooker. Cook on High until vegetables are tender, about 2 hours.

Whisk milk and flour together in a bowl until smooth; stir into slow cooker until thickened. Cook on High for 2 hours more.

Mash potatoes in slow cooker to desired thickness and consistency; stir in ham and cream cheese. Simmer soup until cream cheese has melted, soup is thick and creamy, and ham is heated through, 30 to 60 minutes more.