Adobe stopped updating Flash for Android in 2013. The most recent version of Flash for Android is 11.1.115.81 however for desktop operating systems the current version is 25.0.0.171. So yes many sites that require Flash will detect that the version of Flash installed on Android is very old and may be incompatible with the site.

As kbrosnan mentioned that adobe stopped providing updates for the Android but you can still download that from their official website or from Apk mirror* (it's an external link and downloading files from this site may be harmful). You could download the older versions. If you do not wish to download the flash player, there are few browsers free to download from Google play which have inbuilt flash player and can lose websites sites needing flash player (they can even run flash games online but are too laggy to use).