What is the best way to get to the Dunhuang?

Flying or taking trains are both good. The fast way is to fly to reach there.
If you want to enjoy the beautiful scenery along the road, I suggest you to take trains to reach from Xian.

You could choose classic way the Silk Road from Xi an to DH city,after you start from Xian you could take train been to Lanzhou city. because lanzhou city is The provincial capital city for Lanzhou.
Or you could choose rent to car from lanzhou to DH city.That is amazing trip.