I'm from Malaysia to Linxia, what is the fastest way to get there?

Will you start from Kuala Lumpur? If yes, you can take a flight to Guangzhou Baiyun Airport first and then transfer the plane to Lanzhou Airport. After arriving, take airport shuttle bus to get to Airport Ticket Office first. The ticket fare is CNY 30 per person. Then take a taxi to South Bus Station. There are many direct coaches that can take you to the destination. The bus schedules are from 07:00 to 19:40. It costs about CNY 45 per person.

Yes, I'll be traveling from Kuala Lumpur. Do you know which airline will fly to Guangzhou from Kuala Lumpur? So, from Guangzhou I'll have to take a local flight to Lanzhou? Do you know which local airline is the best to travel to Lanzhou fro Guangzhou? Thanks.

The flights from Kuala Lumpur are operated by China Southern Airlines, Xiamen Airline and Malaysia Airlines.
After arriving, yes, you are advised to take a domestic flight to Lanzhou. China Eastern Airlines, China Southern Airlines and Air China are recommended. :)