This scripts is for lazy people who want to get rid of all LinkedIn messages at once. This works with the latest LinkedIn 2018. Tested on 15th April 2018

removeTheConvo.js

var removeTheConvo = function()
{
  try{
    
  $(".msg-thread__topcard-btn--icon").click();

  setTimeout(function(){ 
    $(".msg-topcard__full-width-action-button.delete").click();

    setTimeout(function(){ 
      $(".confirm-delete-btn").click();

      setTimeout(function(){ 
        removeTheConvo();

      }, 300);
    }, 300);
  }, 300);
    
  }catch(err){
  setTimeout(function(){ 
    removeTheConvo();

  }, 1000);
  }
};
removeTheConvo();

That doesn't seem to work for me... I get a number or errors...

n {stack: "Error: Attempted to handle event deleteRecord on…n.com/sc/h/br/8gesdixxb0mdd0yupx7pukf2q:1278:384)", description: undefined, fileName: undefined, lineNumber: undefined, message: "Attempted to handle event deleteRecord on <messa…398261248> while in state root.deleted.inFlight. ", …}

any ideas?

Very good! This code only didn´t work to marketing messages.
For this things I have to archive this messages.

Here's an updated one - https://gist.github.com/twhitacre/d4536183c22a2f5a8c7c427df04acc90