I'm not sure what the screenshot you posted is supposed to contain. Yes, Microsoft does embed Flash Player in Internet Explorer and Edge browsers on Windows 10 and all updates are distributed by Microsoft via Windows Updates.
First make sure you have the latest version installed by running Windows Update and installing update KB3133431 if it's available. You can also download it from https://support.microsoft.com/en-us/kb/3133431
Secondly, ensure Flash Player is enabled in the browser and, in the case of Internet Explorer, ensure ActiveX Filtering is disabled: