The flushes counter increments as part of selective packet discard (SPD), which implements a selective packet drop policy on the router's IP process queue. Therefore, it applies to only process switched traffic.
The purpose of SPD is to ensure that important control packets, such as routing updates and keepalives, are not dropped then the IP input queue is full. When the size of the IP input queue is between the minimum and maximum thresholds, normal IP packets are dropped based a certain drop probability. These random drops are called SPD flushes.