Flashing zone lights indicate that whatever sensor was installed in that zone has not been "heard" from by the base in a long time. The sensors all send a "I'm here" message to the base about every hour. When the base doesn't receive this signal the zone light flashes. When you set up your system, make sure and write down on a paper what sensors are installed in what zones. It happens sequentially, so the first sensor you install will be zone 1 the second zone 2 etc etc. This way you will have a record to refer to when a light flashes as to what sensor is having a problem. Common reasons for flashing zone lights are:
1) low battery
2) poor signal reception from sensor to base
3) sensors accidentally installed more than one time in different zones
If you know what zone/sensor is the culprit, simply try cycling the sensor by opening and closing the door/window or triggering the motion sensor. You can also use the test button to do this without having to open anything. If the flashing light goes away, see if the problem recurs. AA batteries aren't too expensive so try replacing the batteries, but do this as quickly as possible as not to loose the unique code that is generated for that sensor. If fresh batteries don't help, I've found moving the base to a higher location and thinking about line of sight to the sensor. Is there anything metal or electrical in that line that could be causing interference? You can also move a sensor unit as high as the wiring will allow to improve reception. AKA put sensors on top of doors, and mount the box as high as possible on the wall above the door as the wire to the contact will allow. I have even read of some people splicing in extra wiring to get it even higher for trouble spots.
If there is a registration problem, such as waiting too long while changing batteries it is possible that the sensor has generated a new code and is no longer recognized/registered with the system. In this case I have heard that once the zone light is flashing, if you move to "install" mode the new code will be registered in that trouble zone without having to reinstall the entire system. I have not tested this myself, but others have stated this.
If you don't have a "zone list", you can get a friend to help you by watching the base as you go around and trigger each sensor to see what zone each one is. When you get to a sensor that doesn't activate a zone light, that would be your problem (don't forget that to view zones 9-16 you have to hold down the bypass button). You could also do this yourself by just opening each door/window and walking back to the base and seeing. You can take motion detectors with you to the base and use the test button to find their zone. Motion detectors are tricky during install. They will install themselves multiple times every time you walk by them and things won't work right. You need to face the motion detectors towards the wall when installing the system so they won't register movement and use the test button on the back to register them.
Hope that answers your question and I haven't given you information you are already familiar with. If so just say "DUH!!!" and smile