See https://jira.atlassian.com/browse/CONF-22996 for discussion on why animated gifs are not supported.
The workaround is to host the animated .gif or .png elsewhere on the web, then add it as a web image:
Insert -> Files and images -> Images from the web
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An easy way to do that is to open a free account with imgur.com or other service. I use a free app on windows called ShareX that can record screen regions as gifs and auto upload to imgur. Then it's just a matter of getting the link for the uploaded file and doing just as Milo suggested. Works great and costs nothing. Perfect for showing users how do things when a screen sharing session is not an option.
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