How To Delete Message From Facebook Messenger?

You can delete a single message at a time from both the mobile app version of Facebook Messenger & the desktop version of Messenger, but you cannot delete multiple messages at once. Keep in mind that deleting a message will only remove it from your side of the conversation; the other user the conversation will still be able to see the message unless they also delete it.

Delete Specific Message in FB Messenger

You're interested in removing only specific messages you've sent, or messages someone sent you, do this

Open Facebook.
Click the Messages icon at the top right of the screen. It's the one between the buttons for friend requests and notifications.
Click the message thread you want to permanently delete so that it pops up at the bottom of the screen.
Tip: You can also open all the threads at once with the See All in Messenger link at the bottom of the pop-up, but if you do that, skip down to item 2 below
Use the small gear icon next to that window's exit button (called Options if you hover your mouse over it) to open a new menu.
Select Delete Conversation from that pop-up menu.

Entire conversation from Facebook Messenger:

When you want to Delete This Entire Conversation? Visit Messenger.com or Facebook.com/messages .

Find the Facebook conversation you want to delete.
On the far right-hand side, next to the recipient's name, click the small gear icon to open a new menu
Click the Delete option.
Click Delete again when you're asked to confirm
Locate the message you want to be deleted.

Note:

Hover your mouse over it so that you can see a small menu show up. What you're looking for is a button that's made up of three small horizontal dots.
If you're deleting a Facebook message that you sent them, the menu will show up to the left of the message. If you're wanting to remove something they sent you, look to the right.
Click the small menu button and then hit Delete once, and then delete again if you're sure you want it deleted.