Since Blue Iris still doesn't offer full-featured update checking functionality for apps/UI3 to use, I spent some time tonight to build a proxy server that can provide the update check function in lieu of an official solution.
This is an unofficial solution and could break at any time, but I intend to fix/maintain it for as long as it is possible and useful.
It is released in UI3-334 and is currently accessible to administrator users via UI3's Main Menu > Server Control panel. A future UI3 update will put this directly into the main menu so it'll be a little more accessible.