If you prefer to travel by air, there is no direct flight from Xian to Chifeng. You can fly from Xian to Beijing first and then transfer another flight to Chifeng. From Xian to Beijing, there are many flights available daily. Full price: CNY1,050.
From Beijing to Chifeng, there is a daily flight:
13:10/14:00, GS7503, Tianjin Airlines Full price: CNY460.

Besides, you can choose to fly from Xian to Hohhot and then to Chifeng; two daily flights are available respectively.
Airfare: Xian-Hohhot, Full price CNY1,060; Hohhot-Chifeng, Full price CNY830

I suggest you take the first route. Because there are many flight and discounted tickets from Xian to Beijing and you can get a much economical airfare.