First seen in 2010, Utilities. This page records what the extension did, whether it is still available, and what to use instead.
What it was
Flash Video Download detected FLV and MP4 streams on any page and offered them for download, including YouTube. Flash based video is gone from the web and YouTube downloading is prohibited on the Web Store, so the extension is history.
No longer available
Extensions that download YouTube videos or audio are prohibited by the Chrome Web Store's developer policies, so this extension was never carried by the store and is not distributed here. Downloading YouTube content is also against YouTube's terms of service. The list below shows the video downloaders the store does permit; they work on sites other than YouTube.
Current alternatives
The extensions the Chrome Web Store ranks highest for "video downloader extension" today.