...I am not sure about other root file explorers I think super manager has a file explorer in it but I don't know how it works or if it can change permissions. You may also be able to chmod the file in terminal emulator (free on market)
open terminal and type the following without the quotes
"su"
"chmod 000 /data/data/com.android.browser/app_plugins/com.adobe.flashplayer/.macromedia/Flash_Player/config.data"
then press back to exit terminal
press enter after su and it will prompt for superuser access, the second command is removing all permissions from the file press enter after the second command
To fix Dolphin Browser HD, I ended up downloading "File Expert" (for free) which had root access and the ability to change permissions, and navigated with that file manager to /data/data/mobi.mgeek.TunnyBrowser/app_plugins/com.adobe.flashplayer/.macromedia/Flash_Player/config.data
Edit: Wormdoes, thanks anyway for finding that deal, but I had already found File Expert, fixed the issue, and started a post about it before seeing your post!
For anyone else who reads this to find a fix:
I just had to go into the file manager's settings and enable root access stuff (Menu>More>File Explorer Settings>Check the box at the bottom for Root Explorer), hit the "back" button in the app itself a few times (not the phone's back button) to get to the first "data" folder, navigated to the config file as per the file address above, long pressed the config.data file to bring up options, then went to File Operations>Permission and then unchecked all the permission boxes. Loaded up Dolphin HD (after following Wormdoes' advice about changing the user agent) and was able to watch flash videos without a hassle!
Edit2: Could this be added to a sticky as a HOW TO for people with this issue? Seem to be fairly common, and flash 10.3 is acknowledged as an issue on the CM7 OP... just a suggestion.
Just a side note, I could not find the path for the stock browser as indicated above because app_plugin was missing. I'm not sure why it didn't create this directory when I tried to access flash on the default browser. Anyway, it works for Dolphin HD which is a great browser.