From Xian to Kashgar, there are no direct trains. But you could transfer at Turpan or Urumqi. And it is said that only the hard seats or soft seats takers on common trains could get off at the intermediate train station and then go on the trip on the next day. But passengers also need to make a change at the train station before continuing the trip.

The way for you is to take train to turpan and spend some time there like 2days because turpan has lots of things like underground water channel, gaochang ancient city, jiaohe, and grotto`s, and grape vally as well. then take train to kashgar. it is 21hrs from turpan to kashgar and you can spend 2days in the city and one day trip to karakoram highway, the lake karakol is on KKH. you can spend night there even in a kyrgyz yurt as well then back to city, you can do one day or two days trip to the desert of Taklimakan as well. Then to Urumqi by the train 24hours or flight with one and half hours; In Urumqi, you need to see the museum of the region. Then take train or take bus, or fly to almaty.

All the best. Good luck with your trip.