You may set in the following node of "server.xml":
<message-logs type="2">
<public-message exportPath="..\client\message" url="message" button="On" enable="On"></public-message>
<private-message exportPath="..\client\message" enable="On"></private-message>
</message-logs>
change "enable="On"" into "enable="Off"",save and then restart 123flashchat to make it effective.