To find flights, we find the following flight search engines most useful: Dohop, Skyscanner, Kayak. Combine them for maximum effect. If you are planning a multi-country trip around the Silk Road, the following places are well-connected to the rest of the world, making them good hubs to start and end your trip: Istanbul, Tblisi, Tehran, Bishkek, Almaty, Urumqi.
Flying into Afghanistan, you have a few more options.
How to get to Afghanistan from…
Europe or North America: Direct flights leave from Frankfurt and Moscow with Kam Air, and from Istanbul with Turkish Airlines. Otherwise, flying via Bahrain, Dubai or Abu Dhabi with Kam Air, Safi Air or Flydubai will be the easiest way to get to Afghanistan, or via Sharjah with Airarabia. A final option is via Tehran with Iran Aseman Airlines, who fly to Kabul and Kandahar.
Within Central Asia: With the Almaty – Kabul flight defunct, there is only the Dushanbe – Kabul Kam Air flight left for anyone not in the US military.