The Facebook Help Centre clearly describes the message deletion process.
The following limitations apply,
You will not be able to recover a deleted message. Back them up if necessary.
There is no ‘delete all’ button. Manually deleting all messages can take a significant amount of time.
Browser plugins can automate this process, but the rapid evolution of the Facebook platform means that they soon fall out of date.
The easiest solution is to find someone to do the work for you, perhaps with a little reward for their efforts.