Place potatoes, celery, onion, chicken stock, and parsley into a slow cooker. Season with salt and black pepper. Set cooker on High, cover, and simmer until vegetables are tender, about 2 hours.
Whisk flour with milk in a bowl until smooth. Pour into slow cooker and stir until thickened. Cook on High for 2 more hours.
Mash potatoes in the slow cooker to your desired thickness and consistency; stir in cream cheese and cooked ham. Simmer soup until cream cheese has melted, soup is thick and creamy, and ham is heated through, 30 minutes to 1 hour.