You may request flight following anytime, pre-certificate and after.  My CFI required me to request FF while on my student solos - and sometimes ATC is too busy to grant that service, so don't be too surprised if you are turned down.  It is always based on a workload permitted basis by ATC.  

Another tip - while you are a student pilot, always identify yourself as a student in your flight following request.  ATC does in fact go out of their way to assist students.  

Nowhere is this written down, but I would not request FF for a very short flight.  To me that is just annoying to the controller.  But that may just be me.  -Skip Miller