I notice that you deal with - according to its extension - a rich text format file. Some of my comments depend on that.
You can just use the modification ("write") timestamp of the file itself. If you use the Properties display from MS Word, the timestamps displayed are those of the file: creation and access of the specific copy you are viewing (differs in case the file has been copied from those of the original), modification (same as the original). They are not from some hidden part of the file.
If you do not want to depend on the file's external properties, thus want to record the timestamp in its content, the primary issue is file format.
Inserting a timestamp into a plain text file is, per se, simple:
echo %_date %_time >>! history.log
(Note the exclamation mark ! following the redirection symbol - I use noclobber mode, this overrides the need to have a file to which to concatenate.)
To insert the timestamp into the content of an RTF file, you need to have some knowledge of RTF encoding so that you can insert the text in some appropriate part of the file in a format that is not hidden. This is not necessarily at the beginning or end, it may need to be somewhere in the middle. Sorry, I cannot help with that...