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#Java 8, 60 59 54 53 bytes

v->{for(;;)System.out.write(Math.random()<.5?47:92);}

-1 byte thanks to @BenjaminUrquhart by replacing print with write, so '/' can be 47.

Explanation:

Try it online (times out after 60 sec).

v->{                     // Method with empty unused parameter and no return-type
  for(;;)                //  Loop indefinitely
    System.out.write(    //   Print:
      Math.random()<.5?  //    If the random decimal value in range [0,1) is below 0.5:
       47                //     Print forward slash
      :                  //    Else:
       92);}             //     Print backward slash