I had hard time to figure this out, but I did it finally and I'm going to post an answer to my own question for others.
So firstly install Flash-Aid firefox plugin, and use it to install stable version of Flash Player. Next download "Linux Flash Player 11.2 Plugin content debugger" from Adobe (it doesn't matter if you have 64-bit Ubuntu). Put the proper files in /usr but libflashplayer.so file use to overwrite /usr/lib/flashplugin-installer/libflashplayer.so .
But it's not all. Next install:
ia32-libs is required for nspluginwrapper to work in our case, and that was part that was hard to find for me.
Restart Firefox, and Flash Player 11 Debug should finally work. At least I can connect to it from IntelliJ IDEA.
I hope this will save some time for someone.
Added: #1 After process you should propably disable Flash-Aid extension, or it can overwrite your plugin.