I have built a knowledgebase in SharePoint for our companies Jira users to consume, is there a way to put a button somewhere on every Jira page that they can click to open that link in a new window?
Not the way you describe, without either writing an App or hacking Jira's source. I wouldn't recommend doing either of those things.
You do have some options, though. Jira Server/Data Center has a feature called Announcement Banner. The idea is to create a banner to alert users to scheduled maintenance or provide a link to your Sharepoint site. You can use HTML to format it and it has the option to display at all times or only to logged in users.
The Agile Boards in Jira also have the ability to display a link in the sidebar. Check the doc on how to configure that. One benefit of this approach is that you can display documentation that is relevant to the individual Board, rather than a generic URL that people will have to search through.
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