How can I permanently delete my chat history from Facebook severs?
your chat history is also on the other side with the ones you chat with. Even you clear from your side it will remain with the other side.
To delete messages in a Facebook conversation, start by opening the conversation that you'd like to delete and at the top right of the dialog box is a gear for your options. Clicking on that will present you with a drop down menu, in which you should select See Full Conversation. This will open a web page whereby you will want to click Actions in the top right again, and select Delete Messages. You will then just have to check which messages that you'd like to delete. You may optionally Delete The Conversation entirely.
Facebook has a support article that may be of interest to you which may be located below.
How do I delete messages from a conversation? - facebook.com
Reading & Deleting Messages
Can I retrieve deleted messages? - facebook.com
Facebook Fast Delete: Delete Facebook Messages Quickly [Chrome]