How can I write to a USB 3 flash drive faster than 15 mb/s?
Depends on the speed of the flash. Most flash drives allow faster read then write since writing to a flash is a "destructive operation"

A site like http://usbspeed.nirsoft.net/ might provide further information.

As an example SSD drives are rates at a number of Input/Output Operations/s (IOPS) commonly read is faster then on even the best most expensive drives.