The following command will clear only non-rooted buffers (main, system ..etc).
adb logcat -c
If you want to clear all the buffers (like radio, kernel..etc), Please use the following commands
adb root
adb logcat -b all -c
or
adb root
adb shell logcat -b all -c
Use the following commands to know the list of buffers that device supports
adb logcat -g
adb logcat -b all -g
adb shell logcat -b all -g