It depends on your need for the data at the end of the day. Do you need to be able to do Audits on the data outside of scrolling through a file. If you don't need to browse the data or store it in perpetuity, then a flat file will be faster than MySQL, most likely, if you are just appending to the end of a file.
If you need the data to be more useful, you'll want to store it in mysql. I would suggest that you structure your table like:
id int timestamp datetime default now() desc varchar
That way you don't have to actually create a timestamp in PHP and just let mysql do the work, then you'll e able to do more complex queries off of your table. But, another consideration you'll want to think about is the volume of the data going into this table, as that will also affect your final decision.