With this method I believe that you will have to choose between an unchangeable "Always On" or "On Demand" in Dolphin, because I think the software only limits your ability to make changes to the Flash setting, and since the default is normally Off when one downloads from the play store, normally one can't activate Flash without getting the slap on the hand "you can't do that" from Dolphin. The trick here is to save a copy of the Dolphin ICS settings which allow Flash use and then restore those on JB.
This is how it worked for me.
1. A device running ICS which probably needs to be rooted.
2. Your device running Jellybean which probably needs to be rooted.
3. Titanium backup on both device
4. A version of the Flash Player apk to side load which you can download (they are still available if you Google search) or a Titanium backed up version that you already made.
Turn off automatic backup from your Google account on your JB device.
On your ICS device install Titanium backup and Dolphin from the market. Open Dolphin, go to settings and turn on Flash content. Exit Dolphin. Open Titanium backup and make a backup of Dolphin and Flash player if that is how you will be getting Flash. Now you need to copy those backup files to your Jellybean device. There are several ways to do so which I won't cover here.
On your Jellybean device uninstall any copies of Dolphin and Flash you may already have on there. You can backup your bookmarks first if you wish but can't do a full backup and restore of all your settings because they will overwrite what we are going to do. Now, with a clean Jellybean, install titanium backup from the market if you don't already have it. Open titanium backup and find that dolphin backup you moved from the ICS device. Restore the app and data. Open Dolphin and go to settings and see that Flash is enabled but don't touch the toggle. Close Dolphin. Now either restore the Flash app in Titanium, or install it from an apk you found on the net
Open Dolphin and you should now be able to use Flash, and pinch zoom.
If it was me I would never touch the flash toggle in Dolphin, and I wouldn't let Dolphin update either until we know the newer versions will work as well.
Your mileage may vary, but this worked for me. "Thanks" are appreciated if this works for you.
Good luck and please excuse any typos or mistakes as I was typing this in the car as my daughter was driving (scary)
UPDATE: This method works for Dolphin Beta Browser as well which has improved HTML5 compatibility.
UPDATE See post 3 and post 4 below for possible other methods to get it working without Titanium backup.
As gjc found, deleting the file /data/data/com.dolphin.browser.lab.en/shared_prefs/com.dolphin.browser.lab.en_preferences.xml may allow Dolphin Beta Browser to regenerate the file setting Flash to "On Demand"
As I found below, deleting the file data/data/mobi.mgeek.TunnyBrowser/shared_prefs/mobi.mgeek.TunnyBrowser_preferences.xml may allow the normal Dolphin Browser to regenerate the file setting Flash to "Always On"
So basically, this has allowed me to use Dolphin Browser to browse with Always On and Dolphin Beta Browser for when I wish to browse with the setting "On Demand" which, if not the best of all worlds, at least allows us to use Flash as we see fit.
Some testing and confirmation from others would be nice on these methods as what works for us may not necessarily work for you.