You don't download a licence, you get the key in the licence page on the my.atlassian.com account and paste it into the licence box once Agile is installed.
Justin is correct about where and how you "download" the plugin - go to "manage addons" in admin and look there. If you have the plugin installed, it will be there, and noted as needing an update if it's an old version. If you don't have it installed, type "Agile" into the search box and click to install it.
They are not in the "Manage Add-ons" section of my marketplace account. My account wasn't the original account that did the download. I was added as a technical contact for each of the licenses, so I can see the "download" link under each license. This download link is not for the license, it's for the software/plugin and it takes you to the marketplace where you can download, but there's no where to download if you are a current customer. Note that this works for JIRA, but no other plugin/add-on.
Justin, it was a misunderstanding. Marketplace.atlassian.com also has a page for "manage add-ons". I assumed this was what you meant. You are correct that you can download it through JIRA > Administration > Manage-Addons.
Here are Atlassian instructions for downloading JIRA: https://confluence.atlassian.com/display/AGILE/JIRA+Agile+Installation+and+Upgrade+Guide
The JIRA Agile Developer license is available via your My.Atlassian Account.
...PermissionsStartOnly=true User=www-data Group=www-data ExecStart=/opt/jira/bin/startup.sh ExecStop=/opt/jira/bin/shutdown.sh TimeoutStartSec=120 TimeoutStopSec=600 PrivateTmp=true [Install] WantedBy...
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