For anyone out there experiencing trouble viewing Flash videos due to the latest Android 4.4 (KitKat) update, here is a method that worked on my phone (LG-G2) and should work on any Android 4.4 device. (Neither Puffin nor Photon browsers worked for me)
I only had success after installing the Dolphin Browser and a modified version of Flash (which accommodates the changes in KitKat).
Youtube video tutorial (provided by AndroidRootz.com):
Step-by-step instructions (provided by same):
Having this ability has really helped me fit some extra study time into the day. Hope it can do the same for you.