Outlook Desktop for Windows add-in runs in iFrame of IE Web browser control. To clean up the cache of the add-in open IE browser, go to settings and remove cache. Re-launch your add-in and it should be as good as new.
Outlook for web user may run under supported browsers. In this case go to settings of the web browser used and remove the cache of this browser.
Outlook Desktop for Mac add-in runs under some kind of variation of web browser control (built in with Office 2016 for Mac) and how to remove cache over here is still puzzle for me.
If your application uses RoamingSettings object, take a look if you saveAsync any custom properties and remove them as you need with following saveAsync.
EDIT:
Of cause the described methods above are for your/QA/dev use only. For your customers you, as developer, has to take care of the cache for the files you have changed, when posting new release. As your add-in is nothing else as website, use web technology to re-fresh cache of the browser. There are many ways to achieve that. For example you may change location of the files for new release ...
<script src="/v1.0/Commands.js" type="text/javascript"></script>
<script src="/v1.1/Commands.js" type="text/javascript"></script>
or add some random parameter to the sources file ...
<script src="Commands.js?version=a56b34a87" type="text/javascript"></script>
and so on. Those simple methods will force browser to reload the file content.
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