Flash Player for Android is no longer available. For more information, see here:
Android users can still download and install Flash Player from the Archived Flash Player Versions page on the Adobe website.
Please refer : http://forums.adobe.com/thread/1061194
Please see this page for a list of all certified devices:Flash Player Certified Devices
I highly recommend Ocean Browser for S4.
Right after realising that stock browser does not support flash, I switched to use this great thing.
Before this one is for tablets only (mostly Nexus 10 users) but now also for phones.
read this step by step tutorial : adobe flash player for samsung galaxy s4