The new Flash Player is installed simultaneously with installation of Yandex.Browser. The installation window has the option Install Adobe Flash Player, which is selected by default.
If you don't turn off this option, Yandex.Browser initiates installation of Adobe Flash Player. You will need to agree to the UAC requirements and go through all the steps for installing the plug-in.
The plug-in will be updated automatically, but only after you have agreed to allow updates.