To duplicate a chat window layout from another character, go to the Chat page in the utility for the character that needs the layout. It will look roughly like the composite mock-up image below. Choose the character with the "good" layout from the dropdown on the right-hand side then click Replace. The chat window layout will be duplicated without copying any of the other character settings.
Chat window layouts come from server
_eq2_uisettings.xml files which are not DarqUI customizations. The utility is simply copying and pasting the appropriate blocks of XML from one uisettings file to another. Please post again if you are still unable to duplicate chat layouts.