If you see "Only with Firefox" this means this extension requires an up-to-date version of Firefox. TenFourFox is based on version 45, therefore you must use the versions of extensions compatible with FF 45. Scroll down, click "See all versions", then select the most recent compatible version. Do this quickly because Mozilla plans to remove older versions of extensions soon from their archives, then you'll need to use a third-party archive to install extensions for TenFourFox, and so will users of Pale Moon, Waterfox and others.
If DDG isn't listed in Preferences>Search, click "Restore Default Search Engines".
If you navigate to duckduckgo.com you should also have the option via search sidebar to add the search add-on (that is, if you don't already have it). I don't bother anymore with AMO (okay, spellcheck dictionnaries is possibly an exception). It always work this way for me.