Are there nonstop flights from Tashikuergan (HQL) to Kashgar (KHG)?

Yes. China Southern Airlines fly this route. Flight time is about 45m.

Tashikuergan → Kashgar

Tashikuergan Hongqilafu Airport (HQL) to Kashgar Laining International Airport (KHG)・219 km

Nonstop flights available (1 airline). Flight time about 45m. Nonstop return flights also operate.

Times are estimated from distance. Check schedules, frequency and availability with the airline or a booking site.