Go here:
Archived Flash Player versions
Scroll down to Section titled "Flash Player for Android 4.0 archives" and download latest archived version (11.1.115.81 as of 9/12/13).
Transfer the .apk file to the Download folder on your Note 10.1 and launch it to install it.
Go to your app page, find the Flash icon and launch the app.
[EDIT]
Inserted latest version number
[EDIT]
If you get a message that install is blocked for security reasons because app isn't from Play Store, go to Settings>Security>Device Administration>Unknown Sources and check that box.
Should be GTG