Here's a Tampermonkey script that reverses the order of comments (just replace the @match with your JIRA url, keeping the /* at the end):
// ==UserScript==
// @name JIRA Comments
// @namespace http://tampermonkey.net/
// @version 0.1
// @description Reverse order of comments, etc.
// @author Alexander McCabe
// @match https://*.atlassian.net/*
// @grant GM_addStyle
// @run-at document-start
// ==/UserScript==
(function() {
'use strict';
GM_addStyle('#issue_actions_container, .activity-comment { display: flex !important; flex-direction: column-reverse !important; }');
GM_addStyle('.actionContainer { order: 1 !important; }');
})();
Updated May 19 2020 to also reverse order of replies
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