All right, I will uninstall the flash players I have tried and then see if I can duplicate your success.
Good luck, with Dolphin and Puffin, you should have a couple of browsers that will give you FP content. And I looked back at your original post and see that your Note 3 uses Android 4.4.2, which is the same software version I have in a different make phone, so the available FP version should work.
I guess you have some good, for certain Flash Player content to test with? I use it mostly for sporting events.