Невозможно вызвать инициализатор для типа "String" со списком аргументов типа "(RemoteConfigValue)"

Пожалуйста, прочтите документация

class RemoteConfigValue : NSObject, NSCopying

This class provides a wrapper for Remote Config parameter values, with methods to get parameter values as different data types.

Так что вам нужно написать что-то вроде этого

if let cities = document.data()!["cities"] as? [[String:Any]] { // cities is obviously an array of dictionaries
   for city in cities { // don't use index based loops if you actually don't need the index
       if let cityName = city["cityName"] as? RemoteConfigValue {
          print(cityName.stringValue)
       }
   }
}

Попробуй это

let currentDocument = db.collection("countries").document("United States")

        currentDocument.getDocument { (document, error) in
            if let document = document, document.exists {
                let cities = document.data()!["cities"] // This grabs data from a Firebase object named `cities`, inside the object there are arrays that have two pieces of data (e.g. ["cityName" : "New York", "currentTemperature" : 38])
                for i in 0..<cities!.count {
                    if let cityName = cities[i]["cityName"]! as? String {
                      print(cityName)
                    }
                }
            } else {
                print("Document does not exist")

            }
        }