Based on the given documentation, I have tried to use Timestamper Java API to access the build log including the plain timestamps. 

BufferedReader reader = TimestamperAPI.get().read(currentBuild,"time=HH:mm:ss")

But, I am receiving an empty buffer.

After checking the out timestamper plug-in code and debugging the code, I understood that we need to pass "appendLog" param also to get the proper BufferedReader. So the modified code I am using right now is something like below.

BufferedReader reader = TimestamperAPI.get().read(currentBuild,"time=HH:mm:ss&appendLog")